Disclaimer: The purpose of the Open Case Studies project is to demonstrate the use of various data science methods, tools, and software in the context of messy, real-world data. A given case study does not cover all aspects of the research process, is not claiming to be the most appropriate way to analyze a given data set, and should not be used in the context of making policy decisions without external consultation from scientific experts.
A variety of different sources contribute different types of pollutants to what we call air pollution. Some sources are natural while others are anthropogenic (human derived):
See [here])http://www.redlogenv.com/worker-safety/part-1-dust-and-particulate-matter) for more detail on the types of pollutants in the air.
Air pollution particulates are generally described by their size.
There are 3 major categories:
Large Coarse Particulate Mater - has diameter of >10 micrometers (10 µm)
Coarse Particulate Mater (called PM10-2.5) - has diameter of between 2.5 µm and 10 µm
Fine Particulate Mater (called PM2.5) - has diameter of < 2.5 µm
PM10 includes any particulate mater <10 µm (both coarse and fine particulate mater)
Here you can see how these sizes compare with a human hair:
The following plot and table show the relative sizes of these different pollutants in micrometers(µm):
This table shows how deeply some of the smaller fine particles can penetrate within the human body:
Exposure to air pollution is associated with higher rates of mortality in older adults and is known to be a risk factor for many diseases and conditions including but not limited to:
See this review article for more information about sources of air pollution and the influence of air pollution on health.
Historically epidemiological studies would assess the influence of air pollution on health outcomes by relying on a number of monitors located around the country. However as can be seen in the following figure, these monitors remain to be relatively sparse in certain regions of the country. Furthermore, dramatic differences in pollution rates can be seen even within the same city.
This lack of granularity in air pollution monitoring has hindered our ability to discern the full impact of air pollution on health and to identify at-risk locations.
An article published in the Environmental Health journal dealt with this issue by using data about population density, road density, among other features to model or predict air pollution levels at a more localized scale using machine learning methods.
Yanosky, J. D. et al. Spatio-temporal modeling of particulate air pollution in the conterminous United States using geographic and meteorological predictors. Environ Health 13, 63 (2014).
The authors of this article state that:
“Exposure to atmospheric particulate matter (PM) remains an important public health concern, although it remains difficult to quantify accurately across large geographic areas with sufficiently high spatial resolution. Recent epidemiologic analyses have demonstrated the importance of spatially- and temporally-resolved exposure estimates, which show larger PM-mediated health effects as compared to nearest monitor or county-specific ambient concentrations.”
The article above explains that machine learning methods can be used to predict air pollution levels when traditional monitoring systems are not available in a particular area or when there is not enough spatial granularity with current monitoring systems. We will use similar methods to predict annual air pollution levels spatially within the US.
Our main question:
In this case study, we will walk you through importing data from CSV files and performing machine learning methods to predict our outcome variable of interest (in this case annual fine particle air pollution estimates). We will especially focus on using packages and functions from the Tidyverse, and more specifically the tidymodels package/ecosystem primarily developed and maintained by Max Kuhn and Davis Vaughan. This package loads more modeling related packages like rsample, recipes, parsnip, yardstick, and dials. We will also briefly cover the workflows and tune packages. The tidyverse is a library of packages created by RStudio. While some students may be familiar with previous R programming packages, these packages make data science in R especially efficient.
We will begin by loading the packages that we will need:
library(here)
library(readr)
library(dplyr)
library(skimr)
library(summarytools)
library(magrittr)
library(corrplot)
library(ggcorrplot)
library(GGally)
library(tidymodels)# broom, dials, infer, parsnip, purrr, recipes, rsample, tibble, yardstick
library(workflows)
library(tune)
# library(stringr)
# library(purrr)
# library(tibble)
# library(tidyr)
# library(ggplot2)
# library(ggpubr)
# library(forcats)
# library(lmerTest)
# library(car)
# library(ggiraph)
# library(ggforce)
# library(viridis)
# library(cowplot)| Package | Use |
|---|---|
| here | to easily load and save data |
| readr | to import the CSV file data |
| dplyr | to view/arrange/filter/select/compare specific subsets of the data |
| skimr | to get an overview of data |
| summarytools | to get an overview of data in a different style |
| magrittr | to use the %<>% pipping operator |
| corrplot | to make large correlation plots |
| ggcorrplot | also to make large correlation plots |
| GGally | to make smaller correlation plots |
| rsample | to split the data into testing and training sets and to split the training set for cross-validation |
| recipes | to pre-process data for modeling in a tidy and reproducible way and to extract pre-processed data (major functions are recipe() , prep() and various transformation step_*() functions, as well as juice() - extracts final preprocessed training data and bake() - applies recipe steps to testing data). See here for more info. |
| parsnip | an interface to create models (major functions are fit(), set_engine()) |
| yardstick | to evaluate the performance of models |
stringr | to manipulate the text within the PDF of the data
purrr | to perform functions on all columns of a tibble tibble | to create data objects that we can manipulate with dplyr/stringr/tidyr/purrr tidyr | to separate data within a column into multiple columns ggplot2 | to make visualizations with multiple layers ggpubr | to easily add regression line equations to plots forcats | to change details about factors (categorical variables) lmerTest| to perform linear mixed model testing car| to perform Levene’s Test of Homogeneity of Variances ggiraph| to make plots interactive ggforce| to modify facets in plots viridis| to plot in color palette that is easily interpreted by colorblind individuals cowplot | to allow plots to be combined ___
The first time we use a function, we will use the :: to indicate which package we are using. Unless we have overlapping function names, this is not necessary, but we will include it here to be informative about where the functions we will use come from.
The State of Global Air is a report released every year to communicate the impact of air pollution on public health.
The State of Global Air 2019 report which uses data from 2017 stated that:
Air pollution is the fifth leading risk factor for mortality worldwide. It is responsible for more deaths than many better-known risk factors such as malnutrition, alcohol use, and physical inactivity. Each year, more people die from air pollution–related disease than from road traffic injuries or malaria.
The report also stated that:
In 2017, air pollution is estimated to have contributed to close to 5 million deaths globally — nearly 1 in every 10 deaths.
##### [source]
The State of Global Air 2018 report using data from 2016 which separated different types of air pollution, found that particulate pollution was particularly associated with mortality.
The 2019 report shows that the highest levels of fine particulate pollution occurs in Africa and Asia and that:
More than 90% of people worldwide live in areas exceeding the World Health Organization (WHO) Guideline for healthy air. More than half live in areas that do not even meet WHO’s least-stringent air quality target.
Looking at the US specifically, air pollution levels are generally improving. The US Environmental Protection Agency (EPA) also releases a report about air pollution levels called Our Nation’s Air.
However, air pollution continues to contribute to health risk for Americans, in particular in regions with higher than national average rates of pollution that actually at time exceed the world health organization’s recommended level. Thus it is necessary to obtain high spatial granularity in estimates of air pollution in order to identify locations where populations are experiencing harmful levels of exposure.
You can see that current air quality conditions at this website and you will notice variation across different cities.
Here were the conditions in Topeka Kansas when this was written:
It reports particulate values using what is called the Air Quality Index scale (AQI), this calculator indicates that 114 AQI is equivalent to 40.7 ug/m3 and is considered unhealthy for sensitive individuals. Thus some areas very much exceed the World Health Organization (WHO) annual exposure guideline (10 ug/m3) at certain times and this may adversely affect the health of people living in these locations.
Furthermore, adverse health effects have been associated with populations experiencing higher pollution exposure despite the levels being below suggested guidelines. Secondly, it appears that the composition of the particulate mater and the influence of other demographic factors may make specific populations more at risk for adverse health effects due to air pollution. See this article for more details.
The monitor data that we will use in this case study comes from a system of monitors in which roughly 90% are located within cities. Thus there is an equity issue in terms of capturing the air pollution levels of more rural areas. Therefore, to get a better sense of the pollution exposures for the individuals living in these areas, methods like machine learning can be very useful to estimate air pollution levels in areas with little to no monitoring.
Indeed, machine learning methods are in fact used to be able to estimate air pollution in these low monitoring areas so that we can make a map like this where we have annual estimates for all of the contiguous US:
This is what we aim to achieve in this case study.
There are some important considerations regarding this data analysis to keep in mind:
The data in our analysis does not include information about the composition of particulate mater. Different types of particulates may be more benign or deleterious for health outcomes.
Outdoor pollution levels are not necessarily an indication of of individual exposures. People spend differing amounts of time indoors and outdoors and are exposed to different pollution levels indoors. People are now developing personal monitoring systems to track air pollution levels on the personal level.
Our analysis will use annual mean estimates, however pollution levels can vary greatly by season, day and even hour. There are data sources that have finer levels of temporal data, however we are interested in long term exposures, as these appear to be the most influential for health outcomes, so we chose to use annual level data.
In Machine Learning for prediction, there are two main types of variables:
The outcome variable is what are trying to predict. In building our model we actually have the outcome variable data, but we want to see how well our predictor variables can explain the variation in our outcome data. This gives us a sense of how well we can use the predictor variable data to predict our outcome variable levels when we in fact do not have data about the outcome.
As a simpler example, imagine that we have data about the sales and characteristics of cars from last year and we want to predict which cars might sell well this year. We do not have the sales data yet for this year, but we do know the characteristics of our cars for this year. We can use a model of the characteristics that explained sales last year to estimate what cars might sell well this year. In this case, our outcome variable is the sale performance of the cars, while the different characteristics of the cars make up our predictor or explanatory variables.
In this case study, we will evaluate air pollution monitor data of fine particulate mater (PM2.5) in the contiguous US from 2008, as well as data about population density, road density, urbanization levels, and NASA satellite data to develop models to predict localized air pollution levels.
The monitor data will be our outcome variable. We want to determine if we can predict air pollution levels based on other types of data, like road density and population density to see if we can use these data to predict air pollution in areas where there are no monitors.
The monitor data that we will be using comes from gravimetric monitors operated by the US Enivornmental Protection Agency (EPA). These monitors use a filtration system to specifically capture fine particulate matter. The weight of this matter is manually measured daily or weekly. See here for the EPA standard operating procedure for PM gravimetric analysis in 2008.
Here is an image of what the gravimetric monitors look like:
Gravimetric analysis is also used for emission testing. The same idea applies: a fresh filter is applied and the desired amount of time passes, then the filter is removed and weighed.
There are other monitoring systems that can provide hourly measurements, but we will not be using data from these monitors in our analysis. Gravimetric analysis is considered to be among the most accurate methods.
In our csv, the value column indicates the PM2.5 monitor average for 2008 in mass of fine particles/volume of air for 876 gravimetric monitors. The units are micro grams of fine particulate mater (PM) that is less than 2.5 micrometers in diameter per cubic meter of air - mass concentration (ug/m3). Recall the the WHO exposure guideline is < 10 ug/m3 on average annually for PM2.5.
There are 48 predictor variables with values for each of the 876 monitors included in our outcome variable. The data comes from the US Enivornmental Protection Agency (EPA), the National Aeronautics and Space Administration (NASA), the US Census, and the National Center for Health Statistics (NCHS).
| Variable | Details |
|---|---|
| id | Monitor number – the county number is indicated before the decimal – the monitor number is indicated after the decimal Example: 1073.0023 is Jefferson county (1073) and .0023 one of 8 monitors |
| fips | Federal information processing standard number for the county where the monitor is located – 5 digit id code for counties (zero is often the first value and sometimes is not shown) – the first 2 numbers indicate the state – the last three numbers indicate the county Example: Alabama’s state code is 01 because it is first alphabetically (note: Alaska and Hawaii are not included because they are not part of the contiguous US) |
| Lat | Latitude of the monitor in degrees |
| Lon | Longitude of the monitor in degrees |
| state | State where the monitor is located |
| county | County where the monitor is located |
| city | City where the monitor is located |
| CMAQ | Estimated values of air pollution from a computational model called Community Multiscale Air Quality (CMAQ) – A monitoring system that simulates the physics of the atmosphere using chemistry and weather data to predict the air pollution – Does not use any of the PM2.5 gravimetric monitoring data. (There is a version that does use the gravimetric monitoring data, but not this one!) – Data from the EPA |
| zcta | Zip Code Tabulation Area where the monitor is located – Postal Zip codes are converted into “generalized areal representations” that are non-overlapping – Data from the 2010 Census |
| zcta_area | Land area of the zip code area in meters squared – Data from the 2010 Census |
| zcta_pop | Population in the zip code area – Data from the 2010 Census |
| imp_a500 | Impervious surface measure – Within a circle with a radius of 500 meters around the monitor – Impervious surface are roads, concrete, parking lots, buildings – This is a measure of development |
| imp_a1000 | Impervious surface measure – Within a circle with a radius of 1000 meters around the monitor |
| imp_a5000 | Impervious surface measure – Within a circle with a radius of 5000 meters around the monitor |
| imp_a10000 | Impervious surface measure – Within a circle with a radius of 10000 meters around the monitor |
| imp_a15000 | Impervious surface measure – Within a circle with a radius of 15000 meters around the monitor |
| county_area | Land area of the county of the monitor in meters squared |
| county_pop | Population of the county of the monitor |
| Log_dist_to_prisec | Log (Natural log) distance to a primary or secondary road from the monitor – Highway or major road |
| log_pri_length_5000 | Count of primary road length in meters in a circle with a radius of 5000 meters around the monitor (Natural log) – Highways only |
| log_pri_length_10000 | Count of primary road length in meters in a circle with a radius of 10000 meters around the monitor (Natural log) – Highways only |
| log_pri_length_15000 | Count of primary road length in meters in a circle with a radius of 15000 meters around the monitor (Natural log) – Highways only |
| log_pri_length_25000 | Count of primary road length in meters in a circle with a radius of 25000 meters around the monitor (Natural log) – Highways only |
| log_prisec_length_500 | Count of primary and secondary road length in meters in a circle with a radius of 500 meters around the monitor (Natural log) – Highway and secondary roads |
| log_prisec_length_1000 | Count of primary and secondary road length in meters in a circle with a radius of 1000 meters around the monitor (Natural log) – Highway and secondary roads |
| log_prisec_length_5000 | Count of primary and secondary road length in meters in a circle with a radius of 5000 meters around the monitor (Natural log) – Highway and secondary roads |
| log_prisec_length_10000 | Count of primary and secondary road length in meters in a circle with a radius of 10000 meters around the monitor (Natural log) – Highway and secondary roads |
| log_prisec_length_15000 | Count of primary and secondary road length in meters in a circle with a radius of 15000 meters around the monitor (Natural log) – Highway and secondary roads |
| log_prisec_length_25000 | Count of primary and secondary road length in meters in a circle with a radius of 25000 meters around the monitor (Natural log) – Highway and secondary roads |
| log_nei_2008_pm25_sum_10000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 10000 meters of distance around the monitor (Natural log) |
| log_nei_2008_pm25_sum_15000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 15000 meters of distance around the monitor (Natural log) |
| log_nei_2008_pm25_sum_25000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 25000 meters of distance around the monitor (Natural log) |
| log_nei_2008_pm10_sum_10000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 10000 meters of distance around the monitor (Natural log) |
| log_nei_2008_pm10_sum_15000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 15000 meters of distance around the monitor (Natural log) |
| log_nei_2008_pm10_sum_25000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 25000 meters of distance around the monitor (Natural log) |
| popdens_county | Population density (number of people per kilometer squared area of the county) |
| popdens_zcta | Population density (number of people per kilometer squared area of zcta) |
| nohs | Percentage of people in zcta area where the monitor is that do not have a high school degree – Data from the Census |
| somehs | Percentage of people in zcta area where the monitor whose highest formal educational attainment was some high school education – Data from the Census |
| hs | Percentage of people in zcta area where the monitor whose highest formal educational attainment was completing a high school degree – Data from the Census |
| somecollege | Percentage of people in zcta area where the monitor whose highest formal educational attainment was completing some college education – Data from the Census |
| associate | Percentage of people in zcta area where the monitor whose highest formal educational attainment was completing an associate degree – Data from the Census |
| bachelor | Percentage of people in zcta area where the monitor whose highest formal educational attainment was a bachelor’s degree – Data from the Census |
| grad | Percentage of people in zcta area where the monitor whose highest formal educational attainment was a graduate degree – Data from the Census |
| pov | Percentage of people in zcta area where the monitor is that lived in poverty in 2008 - or would it have been 2007 guidelines??https://aspe.hhs.gov/2007-hhs-poverty-guidelines – Data from the Census |
| hs_orless | Percentage of people in zcta area where the monitor whose highest formal educational attainment was a high school degree or less (sum of nohs, somehs, and hs) |
| urc2013 | 2013 Urban-rural classification of the county where the monitor is located – 6 category variable - 1 is totally urban 6 is completely rural – Data from the National Center for Health Statistics](https://www.cdc.gov/nchs/index.htm){target="_blank"} |
| urc2006 | 2006 Urban-rural classification of the county where the monitor is located – 6 category variable - 1 is totally urban 6 is completely rural – Data from the National Center for Health Statistics |
| aod | Aerosol Optical Depth measurement from a NASA satellite – based on the defraction of a laser – used as a proxy of particulate pollution – unit-less - higher value indicates more pollution – Data from NASA |
Many of these predictor variables have to do with the circular area around the monitor called the “buffer”. These are illustrated in the following figure:
We have one CSV file that contains both our single outcome variable and all of our predictor variables.
Let’s import our data into R now so that we can explore the data further. We will call our data object pm for particulate matter.
The first step in performing a machine learning analysis is to explore the data to better understand the variables included in the data, as we may learn about important details about the data that we should keep in mind as we try to predict our outcome variable.
First let’s just get a general sense of our data. We can do that using the glimpse() function of the dplyr package (it is also in the tibble package).
We will also use the %>% pipe which can be used to define the input for later sequential steps. This will make more sense when we have multiple sequential steps using the same data object. To use the pipe notation we need to install and load dplyr as well.
For example here we will first grab the pm data object, then we use the glimpse() function on it based on the pipe notation.
Rows: 876
Columns: 50
$ id <dbl> 1003.001, 1027.000, 1033.100, 1049.100, 1…
$ value <dbl> 9.597647, 10.800000, 11.212174, 11.659091…
$ fips <dbl> 1003, 1027, 1033, 1049, 1055, 1069, 1073,…
$ lat <dbl> 30.49800, 33.28126, 34.75878, 34.28763, 3…
$ lon <dbl> -87.88141, -85.80218, -87.65056, -85.9683…
$ state <chr> "Alabama", "Alabama", "Alabama", "Alabama…
$ county <chr> "Baldwin", "Clay", "Colbert", "DeKalb", "…
$ city <chr> "Fairhope", "Ashland", "Muscle Shoals", "…
$ CMAQ <dbl> 8.098836, 9.766208, 9.402679, 8.534772, 9…
$ zcta <dbl> 36532, 36251, 35660, 35962, 35901, 36303,…
$ zcta_area <dbl> 190980522, 374132430, 16716984, 203836235…
$ zcta_pop <dbl> 27829, 5103, 9042, 8300, 20045, 30217, 90…
$ imp_a500 <dbl> 0.01730104, 1.96972318, 19.17301038, 5.78…
$ imp_a1000 <dbl> 1.4096021, 0.8531574, 11.1448962, 3.86764…
$ imp_a5000 <dbl> 3.3360118, 0.9851479, 15.1786154, 1.23114…
$ imp_a10000 <dbl> 1.9879187, 0.5208189, 9.7253870, 1.031646…
$ imp_a15000 <dbl> 1.4386207, 0.3359198, 5.2472094, 0.973044…
$ county_area <dbl> 4117521611, 1564252280, 1534877333, 20126…
$ county_pop <dbl> 182265, 13932, 54428, 71109, 104430, 1015…
$ log_dist_to_prisec <dbl> 4.648181, 7.219907, 5.760131, 3.721489, 5…
$ log_pri_length_5000 <dbl> 8.517193, 8.517193, 8.517193, 8.517193, 9…
$ log_pri_length_10000 <dbl> 9.210340, 9.210340, 9.274303, 10.409411, …
$ log_pri_length_15000 <dbl> 9.630228, 9.615805, 9.658899, 11.173626, …
$ log_pri_length_25000 <dbl> 11.32735, 10.12663, 10.15769, 11.90959, 1…
$ log_prisec_length_500 <dbl> 7.295356, 6.214608, 8.611945, 7.310155, 8…
$ log_prisec_length_1000 <dbl> 8.195119, 7.600902, 9.735569, 8.585843, 9…
$ log_prisec_length_5000 <dbl> 10.815042, 10.170878, 11.770407, 10.21420…
$ log_prisec_length_10000 <dbl> 11.88680, 11.40554, 12.84066, 11.50894, 1…
$ log_prisec_length_15000 <dbl> 12.205723, 12.042963, 13.282656, 12.35366…
$ log_prisec_length_25000 <dbl> 13.41395, 12.79980, 13.79973, 13.55979, 1…
$ log_nei_2008_pm25_sum_10000 <dbl> 0.318035438, 3.218632928, 6.573127301, 0.…
$ log_nei_2008_pm25_sum_15000 <dbl> 1.967358961, 3.218632928, 6.581917457, 3.…
$ log_nei_2008_pm25_sum_25000 <dbl> 5.067308, 3.218633, 6.875900, 4.887665, 4…
$ log_nei_2008_pm10_sum_10000 <dbl> 1.35588511, 3.31111648, 6.69187313, 0.000…
$ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 3.350…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 5.171920, 4…
$ popdens_county <dbl> 44.265706, 8.906492, 35.460814, 35.330814…
$ popdens_zcta <dbl> 145.716431, 13.639555, 540.887040, 40.718…
$ nohs <dbl> 3.3, 11.6, 7.3, 14.3, 4.3, 5.8, 7.1, 2.7,…
$ somehs <dbl> 4.9, 19.1, 15.8, 16.7, 13.3, 11.6, 17.1, …
$ hs <dbl> 25.1, 33.9, 30.6, 35.0, 27.8, 29.8, 37.2,…
$ somecollege <dbl> 19.7, 18.8, 20.9, 14.9, 29.2, 21.4, 23.5,…
$ associate <dbl> 8.2, 8.0, 7.6, 5.5, 10.1, 7.9, 7.3, 8.0, …
$ bachelor <dbl> 25.3, 5.5, 12.7, 7.9, 10.0, 13.7, 5.9, 17…
$ grad <dbl> 13.5, 3.1, 5.1, 5.8, 5.4, 9.8, 2.0, 8.7, …
$ pov <dbl> 6.1, 19.5, 19.0, 13.8, 8.8, 15.6, 25.5, 7…
$ hs_orless <dbl> 33.3, 64.6, 53.7, 66.0, 45.4, 47.2, 61.4,…
$ urc2013 <dbl> 4, 6, 4, 6, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ urc2006 <dbl> 5, 6, 4, 5, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ aod <dbl> 37.36364, 34.81818, 36.00000, 33.08333, 4…We can see that there are 876 monitors and that we have 50 total variables - one of which is the outcome. In this case our outcome variable is called value.
Notice that some of the variables that we would think of as factors (categorical) are currently of class double as indicated by the <dbl> just to the right of the column names/variable names in the glimpse() output. For example the monitor ID (id), the Federal Information Processing Standard number for the county where the monitor was located (fips), as well as the zcta
Let’s convert these variables into factors. We can do this using the mutate_at() function of the dplyr package and the as.factor() base function.
In this case we are also using the magrittr assignment pipe or double pipe that looks like this %<>% of the magrittr package. This allows us use the pm data as input but also reassign the output to the same data object name.
Rows: 876
Columns: 50
$ id <fct> 1003.001, 1027.0001, 1033.1002, 1049.1003…
$ value <dbl> 9.597647, 10.800000, 11.212174, 11.659091…
$ fips <fct> 1003, 1027, 1033, 1049, 1055, 1069, 1073,…
$ lat <dbl> 30.49800, 33.28126, 34.75878, 34.28763, 3…
$ lon <dbl> -87.88141, -85.80218, -87.65056, -85.9683…
$ state <chr> "Alabama", "Alabama", "Alabama", "Alabama…
$ county <chr> "Baldwin", "Clay", "Colbert", "DeKalb", "…
$ city <chr> "Fairhope", "Ashland", "Muscle Shoals", "…
$ CMAQ <dbl> 8.098836, 9.766208, 9.402679, 8.534772, 9…
$ zcta <fct> 36532, 36251, 35660, 35962, 35901, 36303,…
$ zcta_area <dbl> 190980522, 374132430, 16716984, 203836235…
$ zcta_pop <dbl> 27829, 5103, 9042, 8300, 20045, 30217, 90…
$ imp_a500 <dbl> 0.01730104, 1.96972318, 19.17301038, 5.78…
$ imp_a1000 <dbl> 1.4096021, 0.8531574, 11.1448962, 3.86764…
$ imp_a5000 <dbl> 3.3360118, 0.9851479, 15.1786154, 1.23114…
$ imp_a10000 <dbl> 1.9879187, 0.5208189, 9.7253870, 1.031646…
$ imp_a15000 <dbl> 1.4386207, 0.3359198, 5.2472094, 0.973044…
$ county_area <dbl> 4117521611, 1564252280, 1534877333, 20126…
$ county_pop <dbl> 182265, 13932, 54428, 71109, 104430, 1015…
$ log_dist_to_prisec <dbl> 4.648181, 7.219907, 5.760131, 3.721489, 5…
$ log_pri_length_5000 <dbl> 8.517193, 8.517193, 8.517193, 8.517193, 9…
$ log_pri_length_10000 <dbl> 9.210340, 9.210340, 9.274303, 10.409411, …
$ log_pri_length_15000 <dbl> 9.630228, 9.615805, 9.658899, 11.173626, …
$ log_pri_length_25000 <dbl> 11.32735, 10.12663, 10.15769, 11.90959, 1…
$ log_prisec_length_500 <dbl> 7.295356, 6.214608, 8.611945, 7.310155, 8…
$ log_prisec_length_1000 <dbl> 8.195119, 7.600902, 9.735569, 8.585843, 9…
$ log_prisec_length_5000 <dbl> 10.815042, 10.170878, 11.770407, 10.21420…
$ log_prisec_length_10000 <dbl> 11.88680, 11.40554, 12.84066, 11.50894, 1…
$ log_prisec_length_15000 <dbl> 12.205723, 12.042963, 13.282656, 12.35366…
$ log_prisec_length_25000 <dbl> 13.41395, 12.79980, 13.79973, 13.55979, 1…
$ log_nei_2008_pm25_sum_10000 <dbl> 0.318035438, 3.218632928, 6.573127301, 0.…
$ log_nei_2008_pm25_sum_15000 <dbl> 1.967358961, 3.218632928, 6.581917457, 3.…
$ log_nei_2008_pm25_sum_25000 <dbl> 5.067308, 3.218633, 6.875900, 4.887665, 4…
$ log_nei_2008_pm10_sum_10000 <dbl> 1.35588511, 3.31111648, 6.69187313, 0.000…
$ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 3.350…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 5.171920, 4…
$ popdens_county <dbl> 44.265706, 8.906492, 35.460814, 35.330814…
$ popdens_zcta <dbl> 145.716431, 13.639555, 540.887040, 40.718…
$ nohs <dbl> 3.3, 11.6, 7.3, 14.3, 4.3, 5.8, 7.1, 2.7,…
$ somehs <dbl> 4.9, 19.1, 15.8, 16.7, 13.3, 11.6, 17.1, …
$ hs <dbl> 25.1, 33.9, 30.6, 35.0, 27.8, 29.8, 37.2,…
$ somecollege <dbl> 19.7, 18.8, 20.9, 14.9, 29.2, 21.4, 23.5,…
$ associate <dbl> 8.2, 8.0, 7.6, 5.5, 10.1, 7.9, 7.3, 8.0, …
$ bachelor <dbl> 25.3, 5.5, 12.7, 7.9, 10.0, 13.7, 5.9, 17…
$ grad <dbl> 13.5, 3.1, 5.1, 5.8, 5.4, 9.8, 2.0, 8.7, …
$ pov <dbl> 6.1, 19.5, 19.0, 13.8, 8.8, 15.6, 25.5, 7…
$ hs_orless <dbl> 33.3, 64.6, 53.7, 66.0, 45.4, 47.2, 61.4,…
$ urc2013 <dbl> 4, 6, 4, 6, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ urc2006 <dbl> 5, 6, 4, 5, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ aod <dbl> 37.36364, 34.81818, 36.00000, 33.08333, 4…Great! Now we can see that these variables are now factors as indicated by <fct> after the variable name.
The skim() function of the skimr package is also really helpful for getting a general sense of your data.
| Name | pm |
| Number of rows | 876 |
| Number of columns | 50 |
| _______________________ | |
| Column type frequency: | |
| character | 3 |
| factor | 3 |
| numeric | 44 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| state | 0 | 1 | 4 | 20 | 0 | 49 | 0 |
| county | 0 | 1 | 3 | 20 | 0 | 471 | 0 |
| city | 0 | 1 | 4 | 48 | 0 | 607 | 0 |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| id | 0 | 1 | FALSE | 876 | 100: 1, 102: 1, 103: 1, 104: 1 |
| fips | 0 | 1 | FALSE | 569 | 170: 12, 603: 10, 261: 9, 107: 8 |
| zcta | 0 | 1 | FALSE | 842 | 475: 3, 110: 2, 160: 2, 290: 2 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| value | 0 | 1 | 10.81 | 2.580000e+00 | 3.02 | 9.27 | 11.15 | 12.37 | 2.316000e+01 | ▂▆▇▁▁ |
| lat | 0 | 1 | 38.48 | 4.620000e+00 | 25.47 | 35.03 | 39.30 | 41.66 | 4.840000e+01 | ▁▃▅▇▂ |
| lon | 0 | 1 | -91.74 | 1.496000e+01 | -124.18 | -99.16 | -87.47 | -80.69 | -6.804000e+01 | ▃▂▃▇▃ |
| CMAQ | 0 | 1 | 8.41 | 2.970000e+00 | 1.63 | 6.53 | 8.62 | 10.24 | 2.313000e+01 | ▃▇▃▁▁ |
| zcta_area | 0 | 1 | 183173481.91 | 5.425989e+08 | 15459.00 | 14204601.75 | 37653560.50 | 160041508.25 | 8.164821e+09 | ▇▁▁▁▁ |
| zcta_pop | 0 | 1 | 24227.58 | 1.777216e+04 | 0.00 | 9797.00 | 22014.00 | 35004.75 | 9.539700e+04 | ▇▇▃▁▁ |
| imp_a500 | 0 | 1 | 24.72 | 1.934000e+01 | 0.00 | 3.70 | 25.12 | 40.22 | 6.961000e+01 | ▇▅▆▃▂ |
| imp_a1000 | 0 | 1 | 24.26 | 1.802000e+01 | 0.00 | 5.32 | 24.53 | 38.59 | 6.750000e+01 | ▇▅▆▃▁ |
| imp_a5000 | 0 | 1 | 19.93 | 1.472000e+01 | 0.05 | 6.79 | 19.07 | 30.11 | 7.460000e+01 | ▇▆▃▁▁ |
| imp_a10000 | 0 | 1 | 15.82 | 1.381000e+01 | 0.09 | 4.54 | 12.36 | 24.17 | 7.209000e+01 | ▇▃▂▁▁ |
| imp_a15000 | 0 | 1 | 13.43 | 1.312000e+01 | 0.11 | 3.24 | 9.67 | 20.55 | 7.110000e+01 | ▇▃▁▁▁ |
| county_area | 0 | 1 | 3768701992.12 | 6.212830e+09 | 33703512.00 | 1116536297.50 | 1690826566.50 | 2878192209.00 | 5.194723e+10 | ▇▁▁▁▁ |
| county_pop | 0 | 1 | 687298.44 | 1.293489e+06 | 783.00 | 100948.00 | 280730.50 | 743159.00 | 9.818605e+06 | ▇▁▁▁▁ |
| log_dist_to_prisec | 0 | 1 | 6.19 | 1.410000e+00 | -1.46 | 5.43 | 6.36 | 7.15 | 1.045000e+01 | ▁▁▃▇▁ |
| log_pri_length_5000 | 0 | 1 | 9.82 | 1.080000e+00 | 8.52 | 8.52 | 10.05 | 10.73 | 1.205000e+01 | ▇▂▆▅▂ |
| log_pri_length_10000 | 0 | 1 | 10.92 | 1.130000e+00 | 9.21 | 9.80 | 11.17 | 11.83 | 1.302000e+01 | ▇▂▇▇▃ |
| log_pri_length_15000 | 0 | 1 | 11.50 | 1.150000e+00 | 9.62 | 10.87 | 11.72 | 12.40 | 1.359000e+01 | ▆▂▇▇▃ |
| log_pri_length_25000 | 0 | 1 | 12.24 | 1.100000e+00 | 10.13 | 11.69 | 12.46 | 13.05 | 1.436000e+01 | ▅▃▇▇▃ |
| log_prisec_length_500 | 0 | 1 | 6.99 | 9.500000e-01 | 6.21 | 6.21 | 6.21 | 7.82 | 9.400000e+00 | ▇▁▂▂▁ |
| log_prisec_length_1000 | 0 | 1 | 8.56 | 7.900000e-01 | 7.60 | 7.60 | 8.66 | 9.20 | 1.047000e+01 | ▇▅▆▃▁ |
| log_prisec_length_5000 | 0 | 1 | 11.28 | 7.800000e-01 | 8.52 | 10.91 | 11.42 | 11.83 | 1.278000e+01 | ▁▁▃▇▃ |
| log_prisec_length_10000 | 0 | 1 | 12.41 | 7.300000e-01 | 9.21 | 11.99 | 12.53 | 12.94 | 1.385000e+01 | ▁▁▃▇▅ |
| log_prisec_length_15000 | 0 | 1 | 13.03 | 7.200000e-01 | 9.62 | 12.59 | 13.13 | 13.57 | 1.441000e+01 | ▁▁▃▇▅ |
| log_prisec_length_25000 | 0 | 1 | 13.82 | 7.000000e-01 | 10.13 | 13.38 | 13.92 | 14.35 | 1.523000e+01 | ▁▁▃▇▆ |
| log_nei_2008_pm25_sum_10000 | 0 | 1 | 3.97 | 2.350000e+00 | 0.00 | 2.15 | 4.29 | 5.69 | 9.120000e+00 | ▆▅▇▆▂ |
| log_nei_2008_pm25_sum_15000 | 0 | 1 | 4.72 | 2.250000e+00 | 0.00 | 3.47 | 5.00 | 6.35 | 9.420000e+00 | ▃▃▇▇▂ |
| log_nei_2008_pm25_sum_25000 | 0 | 1 | 5.67 | 2.110000e+00 | 0.00 | 4.66 | 5.91 | 7.28 | 9.650000e+00 | ▂▂▇▇▃ |
| log_nei_2008_pm10_sum_10000 | 0 | 1 | 4.35 | 2.320000e+00 | 0.00 | 2.69 | 4.62 | 6.07 | 9.340000e+00 | ▅▅▇▇▂ |
| log_nei_2008_pm10_sum_15000 | 0 | 1 | 5.10 | 2.180000e+00 | 0.00 | 3.87 | 5.39 | 6.72 | 9.710000e+00 | ▂▃▇▇▂ |
| log_nei_2008_pm10_sum_25000 | 0 | 1 | 6.07 | 2.010000e+00 | 0.00 | 5.10 | 6.37 | 7.52 | 9.880000e+00 | ▁▂▆▇▃ |
| popdens_county | 0 | 1 | 551.76 | 1.711510e+03 | 0.26 | 40.77 | 156.67 | 510.81 | 2.682191e+04 | ▇▁▁▁▁ |
| popdens_zcta | 0 | 1 | 1279.66 | 2.757490e+03 | 0.00 | 101.15 | 610.35 | 1382.52 | 3.041884e+04 | ▇▁▁▁▁ |
| nohs | 0 | 1 | 6.99 | 7.210000e+00 | 0.00 | 2.70 | 5.10 | 8.80 | 1.000000e+02 | ▇▁▁▁▁ |
| somehs | 0 | 1 | 10.17 | 6.200000e+00 | 0.00 | 5.90 | 9.40 | 13.90 | 7.220000e+01 | ▇▂▁▁▁ |
| hs | 0 | 1 | 30.32 | 1.140000e+01 | 0.00 | 23.80 | 30.75 | 36.10 | 1.000000e+02 | ▂▇▂▁▁ |
| somecollege | 0 | 1 | 21.58 | 8.600000e+00 | 0.00 | 17.50 | 21.30 | 24.70 | 1.000000e+02 | ▆▇▁▁▁ |
| associate | 0 | 1 | 7.13 | 4.010000e+00 | 0.00 | 4.90 | 7.10 | 8.80 | 7.140000e+01 | ▇▁▁▁▁ |
| bachelor | 0 | 1 | 14.90 | 9.710000e+00 | 0.00 | 8.80 | 12.95 | 19.22 | 1.000000e+02 | ▇▂▁▁▁ |
| grad | 0 | 1 | 8.91 | 8.650000e+00 | 0.00 | 3.90 | 6.70 | 11.00 | 1.000000e+02 | ▇▁▁▁▁ |
| pov | 0 | 1 | 14.95 | 1.133000e+01 | 0.00 | 6.50 | 12.10 | 21.22 | 6.590000e+01 | ▇▅▂▁▁ |
| hs_orless | 0 | 1 | 47.48 | 1.675000e+01 | 0.00 | 37.92 | 48.65 | 59.10 | 1.000000e+02 | ▁▃▇▃▁ |
| urc2013 | 0 | 1 | 2.92 | 1.520000e+00 | 1.00 | 2.00 | 3.00 | 4.00 | 6.000000e+00 | ▇▅▃▂▁ |
| urc2006 | 0 | 1 | 2.97 | 1.520000e+00 | 1.00 | 2.00 | 3.00 | 4.00 | 6.000000e+00 | ▇▅▃▂▁ |
| aod | 0 | 1 | 43.70 | 1.956000e+01 | 5.00 | 31.66 | 40.17 | 49.67 | 1.430000e+02 | ▃▇▁▁▁ |
Notice how there is a column called n_missing about the number of values that are missing. It looks like our data is very complete and we do not have any missing data. This is also indicated by the complete_rate variable, which shows the ratio of completeness, in our case all variables have a value of 1 indicating they are fully complete.
The n_unqiue column shows us the number of unique values for each of our columns. We can see that there are 49 states represented in the data, and we know that the data should be of the contiguous states. Let’s take a look to see which states are included:
# A tibble: 49 x 1
state
<chr>
1 Alabama
2 Arizona
3 Arkansas
4 California
5 Colorado
6 Connecticut
7 Delaware
8 District Of Columbia
9 Florida
10 Georgia
11 Idaho
12 Illinois
13 Indiana
14 Iowa
15 Kansas
16 Kentucky
17 Louisiana
18 Maine
19 Maryland
20 Massachusetts
21 Michigan
22 Minnesota
23 Mississippi
24 Missouri
25 Montana
26 Nebraska
27 Nevada
28 New Hampshire
29 New Jersey
30 New Mexico
31 New York
32 North Carolina
33 North Dakota
34 Ohio
35 Oklahoma
36 Oregon
37 Pennsylvania
38 Rhode Island
39 South Carolina
40 South Dakota
41 Tennessee
42 Texas
43 Utah
44 Vermont
45 Virginia
46 Washington
47 West Virginia
48 Wisconsin
49 Wyoming Looks like “District of Columbia” is being included as a state. We can see that indeed Alaska and Hawaii are not included in the data.
Here is another method of looking at the data using the dfSummary() function of the summarytoolspackage. We need to copy and paste the output into the rmarkdown.
Dimensions: 876 x 50
Duplicates: 0
| No | Variable | Stats / Values | Freqs (% of Valid) | Graph | Valid | Missing |
|---|---|---|---|---|---|---|
| 1 | id [factor] |
1. 1003.001 2. 1027.0001 3. 1033.1002 4. 1049.1003 5. 1055.001 6. 1069.0003 7. 1073.0023 8. 1073.1005 9. 1073.1009 10. 1073.101 [ 866 others ] |
1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 866 (98.9%) |
 |
876 (100%) |
0 (0%) |
| 2 | value [numeric] |
Mean (sd) : 10.8 (2.6) min < med < max: 3 < 11.2 < 23.2 IQR (CV) : 3.1 (0.2) |
875 distinct values |  |
876 (100%) |
0 (0%) |
| 3 | fips [factor] |
1. 1003 2. 1027 3. 1033 4. 1049 5. 1055 6. 1069 7. 1073 8. 1089 9. 1097 10. 1101 [ 559 others ] |
1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 8 ( 0.9%) 1 ( 0.1%) 2 ( 0.2%) 1 ( 0.1%) 858 (98.0%) |
 |
876 (100%) |
0 (0%) |
| 4 | lat [numeric] |
Mean (sd) : 38.5 (4.6) min < med < max: 25.5 < 39.3 < 48.4 IQR (CV) : 6.6 (0.1) |
876 distinct values |  |
876 (100%) |
0 (0%) |
| 5 | lon [numeric] |
Mean (sd) : -91.7 (15) min < med < max: -124.2 < -87.5 < -68 IQR (CV) : 18.5 (-0.2) |
876 distinct values |  |
876 (100%) |
0 (0%) |
| 6 | state [character] |
1. California 2. Ohio 3. Illinois 4. Indiana 5. North Carolina 6. Pennsylvania 7. Michigan 8. Florida 9. Georgia 10. Texas [ 39 others ] |
85 ( 9.7%) 44 ( 5.0%) 38 ( 4.3%) 36 ( 4.1%) 35 ( 4.0%) 32 ( 3.7%) 30 ( 3.4%) 29 ( 3.3%) 28 ( 3.2%) 27 ( 3.1%) 492 (56.2%) |
 |
876 (100%) |
0 (0%) |
| 7 | county [character] |
1. Jefferson 2. Cook 3. Hamilton 4. Lake 5. Los Angeles 6. Wayne 7. Washington 8. Cuyahoga 9. Jackson 10. Madison [ 461 others ] |
18 ( 2.1%) 12 ( 1.4%) 11 ( 1.3%) 11 ( 1.3%) 10 ( 1.1%) 10 ( 1.1%) 9 ( 1.0%) 7 ( 0.8%) 7 ( 0.8%) 7 ( 0.8%) 774 (88.4%) |
 |
876 (100%) |
0 (0%) |
| 8 | city [character] |
1. Not in a city 2. New York 3. Cleveland 4. Baltimore 5. Chicago 6. Detroit 7. Milwaukee 8. New Haven 9. Philadelphia 10. Springfield [ 597 others ] |
103 (11.8%) 9 ( 1.0%) 6 ( 0.7%) 5 ( 0.6%) 5 ( 0.6%) 5 ( 0.6%) 5 ( 0.6%) 5 ( 0.6%) 5 ( 0.6%) 5 ( 0.6%) 723 (82.5%) |
 |
876 (100%) |
0 (0%) |
| 9 | CMAQ | Me [numeric] | an (sd) : 8.4 (3) | 60 min < med < max: 1.6 < 8.6 < 23.1 IQR (CV) : 3.7 (0.4) |
1 distinct values |  | 87 | 6 | 0 (100%) |
(0%) |
| 10 | zcta [factor] |
1. 1022 2. 1103 3. 1201 4. 1608 5. 1832 6. 1840 7. 1863 8. 1904 9. 2113 10. 2119 [ 832 others ] |
1 ( 0.1%) 2 ( 0.2%) 1 ( 0.1%) 2 ( 0.2%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 1 ( 0.1%) 864 (98.6%) |
 |
876 (100%) |
0 (0%) |
| 11 | zcta_area [numeric] |
Mean (sd) : 183173481.9 (542598878.5) min < med < max: 15459 < 37653560.5 < 8164820625 IQR (CV) : 145836906.5 (3) |
842 distinct values |  |
876 (100%) |
0 (0%) |
| 12 | zcta_pop [numeric] |
Mean (sd) : 24227.6 (17772.2) min < med < max: 0 < 22014 < 95397 IQR (CV) : 25207.8 (0.7) |
837 distinct values |  |
876 (100%) |
0 (0%) |
| 13 | imp_a500 [numeric] |
Mean (sd) : 24.7 (19.3) min < med < max: 0 < 25.1 < 69.6 IQR (CV) : 36.5 (0.8) |
816 distinct values |  |
876 (100%) |
0 (0%) |
| 14 | imp_a1000 [numeric] |
Mean (sd) : 24.3 (18) min < med < max: 0 < 24.5 < 67.5 IQR (CV) : 33.3 (0.7) |
860 distinct values |  |
876 (100%) |
0 (0%) |
| 15 | imp_a5000 [numeric] |
Mean (sd) : 19.9 (14.7) min < med < max: 0.1 < 19.1 < 74.6 IQR (CV) : 23.3 (0.7) |
870 distinct values |  |
876 (100%) |
0 (0%) |
| 16 | imp_a10000 [numeric] |
Mean (sd) : 15.8 (13.8) min < med < max: 0.1 < 12.4 < 72.1 IQR (CV) : 19.6 (0.9) |
870 distinct values |  |
876 (100%) |
0 (0%) |
| 17 | imp_a15000 [numeric] |
Mean (sd) : 13.4 (13.1) min < med < max: 0.1 < 9.7 < 71.1 IQR (CV) : 17.3 (1) |
870 distinct values |  |
876 (100%) |
0 (0%) |
| 18 | county_area [numeric] |
Mean (sd) : 3768701992.1 (6212829553.6) min < med < max: 33703512 < 1690826566.5 < 51947229509 IQR (CV) : 1761655911.5 (1.6) |
564 distinct values |  |
876 (100%) |
0 (0%) |
| 19 | county_pop [numeric] |
Mean (sd) : 687298.4 (1293488.7) min < med < max: 783 < 280730.5 < 9818605 IQR (CV) : 642211 (1.9) |
564 distinct values |  |
876 (100%) |
0 (0%) |
| 20 | log_dist_to_prisec [numeric] |
Mean (sd) : 6.2 (1.4) min < med < max: -1.5 < 6.4 < 10.5 IQR (CV) : 1.7 (0.2) |
870 distinct values |  |
876 (100%) |
0 (0%) |
| 21 | log_pri_length_5000 [numeric] |
Mean (sd) : 9.8 (1.1) min < med < max: 8.5 < 10.1 < 12 IQR (CV) : 2.2 (0.1) |
586 distinct values |  |
876 (100%) |
0 (0%) |
| 22 | log_pri_length_10000 [numeric] |
Mean (sd) : 10.9 (1.1) min < med < max: 9.2 < 11.2 < 13 IQR (CV) : 2 (0.1) |
687 distinct values |  |
876 (100%) |
0 (0%) |
| 23 | log_pri_length_15000 [numeric] |
Mean (sd) : 11.5 (1.1) min < med < max: 9.6 < 11.7 < 13.6 IQR (CV) : 1.5 (0.1) |
726 distinct values |  |
876 (100%) |
0 (0%) |
| 24 | log_pri_length_25000 [numeric] |
Mean (sd) : 12.2 (1.1) min < med < max: 10.1 < 12.5 < 14.4 IQR (CV) : 1.4 (0.1) |
787 distinct values |  |
876 (100%) |
0 (0%) |
| 25 | log_prisec_length_500 [numeric] |
Mean (sd) : 7 (1) min < med < max: 6.2 < 6.2 < 9.4 IQR (CV) : 1.6 (0.1) |
382 distinct values |  |
876 (100%) |
0 (0%) |
| 26 | log_prisec_length_1000 [numeric] |
Mean (sd) : 8.6 (0.8) min < med < max: 7.6 < 8.7 < 10.5 IQR (CV) : 1.6 (0.1) |
591 distinct values |  |
876 (100%) |
0 (0%) |
| 27 | log_prisec_length_5000 [numeric] |
Mean (sd) : 11.3 (0.8) min < med < max: 8.5 < 11.4 < 12.8 IQR (CV) : 0.9 (0.1) |
852 distinct values |  |
876 (100%) |
0 (0%) |
| 28 | log_prisec_length_10000 [numeric] |
Mean (sd) : 12.4 (0.7) min < med < max: 9.2 < 12.5 < 13.8 IQR (CV) : 1 (0.1) |
867 distinct values |  |
876 (100%) |
0 (0%) |
| 29 | log_prisec_length_15000 [numeric] |
Mean (sd) : 13 (0.7) min < med < max: 9.6 < 13.1 < 14.4 IQR (CV) : 1 (0.1) |
869 distinct values |  |
876 (100%) |
0 (0%) |
| 30 | log_prisec_length_25000 [numeric] |
Mean (sd) : 13.8 (0.7) min < med < max: 10.1 < 13.9 < 15.2 IQR (CV) : 1 (0.1) |
870 distinct values |  |
876 (100%) |
0 (0%) |
| 31 | log_nei_2008_pm25_sum_10000 [numeric] |
Mean (sd) : 4 (2.4) min < med < max: 0 < 4.3 < 9.1 IQR (CV) : 3.5 (0.6) |
828 distinct values |  |
876 (100%) |
0 (0%) |
| 32 | log_nei_2008_pm25_sum_15000 [numeric] |
Mean (sd) : 4.7 (2.2) min < med < max: 0 < 5 < 9.4 IQR (CV) : 2.9 (0.5) |
855 distinct values |  |
876 (100%) |
0 (0%) |
| 33 | log_nei_2008_pm25_sum_25000 [numeric] |
Mean (sd) : 5.7 (2.1) min < med < max: 0 < 5.9 < 9.7 IQR (CV) : 2.6 (0.4) |
860 distinct values |  |
876 (100%) |
0 (0%) |
| 34 | log_nei_2008_pm10_sum_10000 [numeric] |
Mean (sd) : 4.3 (2.3) min < med < max: 0 < 4.6 < 9.3 IQR (CV) : 3.4 (0.5) |
829 distinct values |  |
876 (100%) |
0 (0%) |
| 35 | log_nei_2008_pm10_sum_15000 [numeric] |
Mean (sd) : 5.1 (2.2) min < med < max: 0 < 5.4 < 9.7 IQR (CV) : 2.8 (0.4) |
855 distinct values |  |
876 (100%) |
0 (0%) |
| 36 | log_nei_2008_pm10_sum_25000 [numeric] |
Mean (sd) : 6.1 (2) min < med < max: 0 < 6.4 < 9.9 IQR (CV) : 2.4 (0.3) |
860 distinct values |  |
876 (100%) |
0 (0%) |
| 37 | popdens_county [numeric] |
Mean (sd) : 551.8 (1711.5) min < med < max: 0.3 < 156.7 < 26821.9 IQR (CV) : 470 (3.1) |
564 distinct values |  |
876 (100%) |
0 (0%) |
| 38 | popdens_zcta [numeric] |
Mean (sd) : 1279.7 (2757.5) min < med < max: 0 < 610.3 < 30418.8 IQR (CV) : 1281.4 (2.2) |
840 distinct values |  |
876 (100%) |
0 (0%) |
| 39 | nohs [numeric] |
Mean (sd) : 7 (7.2) min < med < max: 0 < 5.1 < 100 IQR (CV) : 6.1 (1) |
215 distinct values |  |
876 (100%) |
0 (0%) |
| 40 | somehs [numeric] |
Mean (sd) : 10.2 (6.2) min < med < max: 0 < 9.4 < 72.2 IQR (CV) : 8 (0.6) |
230 distinct values |  |
876 (100%) |
0 (0%) |
| 41 | hs [numeric] |
Mean (sd) : 30.3 (11.4) min < med < max: 0 < 30.8 < 100 IQR (CV) : 12.3 (0.4) |
347 distinct values |  |
876 (100%) |
0 (0%) |
| 42 | somecollege [numeric] |
Mean (sd) : 21.6 (8.6) min < med < max: 0 < 21.3 < 100 IQR (CV) : 7.2 (0.4) |
240 distinct values |  |
876 (100%) |
0 (0%) |
| 43 | associate [numeric] |
Mean (sd) : 7.1 (4) min < med < max: 0 < 7.1 < 71.4 IQR (CV) : 3.9 (0.6) |
157 distinct values |  |
876 (100%) |
0 (0%) |
| 44 | bachelor [numeric] |
Mean (sd) : 14.9 (9.7) min < med < max: 0 < 12.9 < 100 IQR (CV) : 10.4 (0.7) |
301 distinct values |  |
876 (100%) |
0 (0%) |
| 45 | grad [numeric] |
Mean (sd) : 8.9 (8.6) min < med < max: 0 < 6.7 < 100 IQR (CV) : 7.1 (1) |
245 distinct values |  |
876 (100%) |
0 (0%) |
| 46 | pov [numeric] |
Mean (sd) : 15 (11.3) min < med < max: 0 < 12.1 < 65.9 IQR (CV) : 14.7 (0.8) |
345 distinct values |  |
876 (100%) |
0 (0%) |
| 47 | hs_orless [numeric] |
Mean (sd) : 47.5 (16.8) min < med < max: 0 < 48.7 < 100 IQR (CV) : 21.2 (0.4) |
464 distinct values |  |
876 (100%) |
0 (0%) |
| 48 | urc2013 [numeric] |
Mean (sd) : 2.9 (1.5) min < med < max: 1 < 3 < 6 IQR (CV) : 2 (0.5) |
1 : 203 (23.2%) 2 : 163 (18.6%) 3 : 228 (26.0%) 4 : 123 (14.0%) 5 : 101 (11.5%) 6 : 58 ( 6.6%) |
 |
876 (100%) |
0 (0%) |
| 49 | urc2006 [numeric] |
Mean (sd) : 3 (1.5) min < med < max: 1 < 3 < 6 IQR (CV) : 2 (0.5) |
1 : 195 (22.3%) 2 : 162 (18.5%) 3 : 221 (25.2%) 4 : 127 (14.5%) 5 : 115 (13.1%) 6 : 56 ( 6.4%) |
 |
876 (100%) |
0 (0%) |
| 50 | aod [numeric] |
Mean (sd) : 43.7 (19.6) min < med < max: 5 < 40.2 < 143 IQR (CV) : 18 (0.4) |
581 distinct values |  |
876 (100%) |
0 (0%) |
We can see that for many variables there are many low values as the distribution shows two peaks, one near zero and another with a higher value. This is true for the imp variables (measures of development), the nei variables (measures of emission sources) and the road density variables. We can also see that the range of some of the variables is very large, in particular the area and population related variables.
In prediction analyses, it is also useful to evaluate if any of the variables are correlated.
Intuitively we can expect some of our variables to be correlated.
Let’s first take a look at all of our numeric variabels with thecorrplot package: The corrplot package is another option to look at correlation among possible predictors. This is a great option if we have many predictors. First we need to create a correlation matrix using the cor() function of the stats package (which is loaded automatically).
library(RColorBrewer)
PM_cor <- cor(pm %>% dplyr::select_if(is.numeric))
corrplot::corrplot(PM_cor, tl.cex = 0.5)
corrplot(PM_cor, diag = FALSE, order = "FPC",
tl.pos = "td", tl.cex = 0.5, method = "color", type = "upper", col = brewer.pal(n = 8, name = "PuOr"))
Using ggcorplot
We can see that the the development variables (imp) variables are correlated with each other as we might expect. We also see that the road density variables seem to be correlated with each other, and the emission variables seem to be correlated with each other. We can take a closer look using the ggcorr() function and the ggpairs() function of the GGally package. To select our variables of interest we can use the select() function with the contains() function of the tidyr package.
First let’s look at the imp/development variables.
Indeed, we can see that imp_a1000 and imp_a500 are perfectly correlated, as well as imp_a10000, imp_a15000.
Now let’s take a look at the road density data:
select(pm, contains("pri")) %>%
ggcorr(palette = "RdBu", hjust = .85, size = 3,
layout.exp=2, label = TRUE)
We can see that while some of the road density variables are highly correlated with one another (or anti-correlated), there arr some variables that are less correlated with one another.
Finally let’s look at the emission variables.
select(pm, contains("nei")) %>%
ggcorr(palette = "RdBu", hjust = .85, size = 3,
layout.exp=2, label = TRUE)
We would also expect the population density data might correlate with some of these variables. Let’s take a look.
pm %>%
select(log_nei_2008_pm25_sum_10000, popdens_county, log_pri_length_10000, imp_a10000) %>%
ggcorr(palette = "RdBu", hjust = .85, size = 3,
layout.exp=2, label = TRUE)
pm %>%
select(log_nei_2008_pm25_sum_10000, popdens_county, log_pri_length_10000, imp_a10000, county_pop) %>%
ggpairs()
Interesting, so these variables don’t appear to be highly correlated, therefore we might need variables from each of the categories to predict our monitor PM2.5 pollution values.
We seem to have some pretty extreme population values though, so let’s see what happens when we take the log value.
pm %>%
mutate(log_popdens_county= log(popdens_county)) %>%
select(log_nei_2008_pm25_sum_10000, log_popdens_county, log_pri_length_10000, imp_a10000) %>%
ggcorr(palette = "RdBu", hjust = .85, size = 3,
layout.exp=2, label = TRUE)
pm %>%
mutate(log_popdens_county= log(popdens_county)) %>%
mutate(log_pop_county = log(county_pop)) %>%
select(log_nei_2008_pm25_sum_10000, log_popdens_county, log_pri_length_10000, imp_a10000, log_pop_county) %>%
ggpairs()
Indeed this increased the correlation, but variables from each of these categories may still prove to be useful for prediction.
Now that we have a sense of what our data is like we can get started with data analysis.
To perform our analysis we will be using the tidymodels suite of packages. You may be familiar with the older packages caret or mlr which are also for machine learning and modeling but are not a part of the tidyverse. Max Kuhn describes tidymodels like this:
“Other packages, such as caret and mlr, help to solve the R model API issue. These packages do a lot of other things too: preprocessing, model tuning, resampling, feature selection, ensembling, and so on. In the tidyverse, we strive to make our packages modular and parsnip is designed only to solve the interface issue. It is not designed to be a drop-in replacement for caret. The tidymodels package collection, which includes parsnip, has other packages for many of these tasks, and they are designed to work together. We are working towards higher-level APIs that can replicate and extend what the current model packages can do.”
There are many packages in the tidymodels ecosystem which assist with the various steps of the machine learning process:
This is the overall process:
There are two distinct goals of supervised machine learning:
We will be performing a prediction analysis (which is also refered to as regression), which aims to predict continuous outcome variables given a number of predictors/explanatory variables/features/parameters, as we have already described.
Classification on the other hand aims to discern or predict group identity for a categorical outcome based on a number of predictors/explanatory variables/features/parameters.
The overall process is the same in either case.
The first step after data exploration in machine learning analysis is to split the data into training and testing datasets.
The training dataset will be used to build and tune our model. This is the data that the model “learns” on.
The testing set will be used to evaluate the performance of our model in a more generalizable way. What do we mean by “generalizable”?
Remember that our main goal is to use our model to be able to predict air pollution levels in areas where there are no gravimetric monitors. Therefore, if our model is super good at predicting air pollution with the data that we use to build it, it might not do the best job for the areas where there are few to no monitors. This would cause us to have really good prediction accuracy and we might assume that we were going to do a good job estimating air pollution any time we use our model, but in fact this would likely not be the case. This situation is what we call overfitting .
Overfitting happens when we end up modeling not only the major relationships in our data but also the noise within our data.
If we get fairly good prediction with our testing set then we will know that our model can be applied to other data and will perform fairly well. We will discuss this more later.
We will not touch the testing set until we have completed optimizing our model with the training set. This will allow us to have a less biased evaluation of how well our model can do with other data besides the data used in the training set to build the model. Ideally you would also want a completely independent dataset to further test the performance of your model.
Here is a great description of the differences between testing and training datasets.
We will use the rsample package to perform this step.
Theinitial_split() function allows us to specify how we want to split our data. Typically data is split into 3/4 for training and 1/4 for testing.This is the default proportion and does not need to be specified. However you can change the proportion using the prop argument, which we will do that here for illustrative purposes. You can also specify a variable to stratify by with the strata argument. This is useful if you have imbalanced categorical variables and you would like to intentionally make sure that there are similar number of samples of the rarer categories in both the testing and training sets. Otherwise the split is performed randomly.
The strata argument causes the random sampling to be conducted within the stratification variable. The can help ensure that the number of data points in the training data is equivalent to the proportions in the original data set.
In the case with our dataset, perhaps we would like our training set to have similar proportions of monitors from each of the states as in the initial data. This might be useful if we want our model to be generalizable across all of the states.
We can see that indeed there are different proportions of monitors in each state by using the count() function of the dpyr package.
# A tibble: 49 x 2
state n
<chr> <int>
1 Alabama 24
2 Arizona 17
3 Arkansas 16
4 California 85
5 Colorado 15
6 Connecticut 14
7 Delaware 7
8 District Of Columbia 3
9 Florida 29
10 Georgia 28
11 Idaho 7
12 Illinois 38
13 Indiana 36
14 Iowa 20
15 Kansas 10
16 Kentucky 22
17 Louisiana 17
18 Maine 1
19 Maryland 15
20 Massachusetts 16
21 Michigan 30
22 Minnesota 17
23 Mississippi 12
24 Missouri 13
25 Montana 16
26 Nebraska 7
27 Nevada 4
28 New Hampshire 7
29 New Jersey 23
30 New Mexico 10
31 New York 24
32 North Carolina 35
33 North Dakota 4
34 Ohio 44
35 Oklahoma 10
36 Oregon 17
37 Pennsylvania 32
38 Rhode Island 5
39 South Carolina 14
40 South Dakota 9
41 Tennessee 3
42 Texas 27
43 Utah 14
44 Vermont 4
45 Virginia 20
46 Washington 8
47 West Virginia 14
48 Wisconsin 21
49 Wyoming 12If our dataset were large enough it might be nice then to stratify by state, but our data is unfortunately not large enough. We will show how one would do this though for illustrative purposes. This option is often more important for classification applications of machine learning than it is for prediction.
Since the split is performed randomly, it is a good idea to use the set.seed() base function to ensure that if your rerun your code that your split will be the same next time. We can see the number of monitors in our training, testing, and original data by typing in the name of our split object. The result will look like this: <training data sample number, testing data sample number, original sample number>
<Analysis/Assess/Total>
<584/292/876># If stratifying:
# pm_split_strata <-rsample::initial_split(data = pm, prop = 2/3, strata = "state")Importantly the initial_split function only determines what rows of our pm data frame should be assigned for training or testing, it does not actually split the data.
To extract the testing and training data we can use the training() and testing() functions also of the rsample package.
train_pm <-rsample::training(pm_split)
test_pm <-rsample::testing(pm_split)
# Scroll through the output!
count(train_pm, state)# A tibble: 48 x 2
state n
<chr> <int>
1 Alabama 18
2 Arizona 12
3 Arkansas 14
4 California 54
5 Colorado 12
6 Connecticut 8
7 Delaware 6
8 District Of Columbia 2
9 Florida 18
10 Georgia 17
# … with 38 more rows# A tibble: 48 x 2
state n
<chr> <int>
1 Alabama 6
2 Arizona 5
3 Arkansas 2
4 California 31
5 Colorado 3
6 Connecticut 6
7 Delaware 1
8 District Of Columbia 1
9 Florida 11
10 Georgia 11
# … with 38 more rowsIn tidymodels we will create a recipe, which is a standardized format for a sequence of steps for processing the data.
This can be very useful because it makes testing out different pre-processing steps or different algorithms with the same pre-processing very easy and reproducible.
Creating a recipe specifies how a dataframe of predictors should be created - it specifies what variables to be used and the preprocessing steps but it does not execute these steps or create the dataframe of predictors.
recipe() functionThe first thing to do to create a recipe is to specify which variables we will be using as our outcome and predictors using the recipe() function. In terms of the metaphor of baking, we can think of this as listing our ingredients. The naming convention for recipe object names is *_rec or rec.
In our case recall that our value variable, which is the average annual gravimetric monitor PM2.5 concentration in ug/m3. Our predictors are all the other variables except the monitor ID, which is an id variable.
The reason not to include this variable is because this variable includes the county number and a number designating which particular monitor the values came from of the monitors there are in that county. Since this number is arbitrary and the county information is also given in the data, and the fact that each monitor only has one value in the value variable, nothing is gained by including this variable and it may instead introduce noise. However, it is useful to keep this data to take a look at what is happening later. We will show you what to do in this case in just a bit.
The simplest recipe with no preprocessing steps, would be to simply list the outcome and predictor variables.
We can do so in two ways:
Let’s look at the first way using formula notation, which looks like this:
outcome(s) ~ predictor(s)
If in the case of multiple predictors or a multivariate situation with two outcomes, use a plus sign
outcome1 + outcome2 ~ predictor1 + predictor2
If we want to include all predictors we can use a period like so:
outcome_variable_name ~ .
Now with our data we will start by making a recipe for our training data. In the simplest case we might use all predictors like this:
Data Recipe
Inputs:
role #variables
outcome 1
predictor 49However, to deal with the id variable we could use the update_role() function of the recipes package:
simple_rec <-train_pm %>%
recipes::recipe(value ~ .) %>%
recipes::update_role(id, new_role = "id variable")
simple_recData Recipe
Inputs:
role #variables
id variable 1
outcome 1
predictor 48We could also specify the outcome and predictors in the same way as the id variable. Please see here for examples of other roles for variables. The role can be actually be any value.
The order is important here, as we first make all variables predictors and then override this role for the outcome and id variable. We will use the everything() function of the dplyr package to start with all of the variables in train_pm.
simple_rec <-recipe(train_pm) %>%
update_role(everything(), new_role = "predictor")%>%
update_role(value, new_role = "outcome")%>%
update_role(id, new_role = "id variable")
simple_recData Recipe
Inputs:
role #variables
id variable 1
outcome 1
predictor 48If we want to take a look at our formula from our recipe we can do use the formula() function of the stats package.
value ~ fips + lat + lon + state + county + city + CMAQ + zcta +
zcta_area + zcta_pop + imp_a500 + imp_a1000 + imp_a5000 +
imp_a10000 + imp_a15000 + county_area + county_pop + log_dist_to_prisec +
log_pri_length_5000 + log_pri_length_10000 + log_pri_length_15000 +
log_pri_length_25000 + log_prisec_length_500 + log_prisec_length_1000 +
log_prisec_length_5000 + log_prisec_length_10000 + log_prisec_length_15000 +
log_prisec_length_25000 + log_nei_2008_pm25_sum_10000 + log_nei_2008_pm25_sum_15000 +
log_nei_2008_pm25_sum_25000 + log_nei_2008_pm10_sum_10000 +
log_nei_2008_pm10_sum_15000 + log_nei_2008_pm10_sum_25000 +
popdens_county + popdens_zcta + nohs + somehs + hs + somecollege +
associate + bachelor + grad + pov + hs_orless + urc2013 +
urc2006 + aod
<environment: 0x7fddad2b8900>We can also view our recipe in more detail using the base summary() function.
# A tibble: 50 x 4
variable type role source
<chr> <chr> <chr> <chr>
1 id nominal id variable original
2 value numeric outcome original
3 fips nominal predictor original
4 lat numeric predictor original
5 lon numeric predictor original
6 state nominal predictor original
7 county nominal predictor original
8 city nominal predictor original
9 CMAQ numeric predictor original
10 zcta nominal predictor original
# … with 40 more rowsrecipe packageThe other thing the recipes package allows for is specifying pre-processing steps using a variety of step*() functions.
This link and this link show the many options for recipe step functions.
There are step functions for a variety of purposes:
All of the step functions look like step_* except for the check functions which look like check_*.
There are several ways to select what variables to apply steps to:
1) tidyselect methods: contains(), matches(), starts_with(), ends_with(), everything(), num_range()
2) based on the type: all_nominal(), all_numeric() , has_type() 3) based on the role: all_predictors(), all_outcomes(), has_role() 4) name - use the actual name of the variable/variables of interest
Let’s try adding some steps to our recipe.
We might consider log transforming our population and area variables (that aren’t densities) - let’s take a look at the range of these variables.
$zcta_area
[1] 15459 8164820625
$zcta_pop
[1] 0 95397
$county_area
[1] 33703512 51947229509
$county_pop
[1] 783 9818605We can see that the range for each of these variables is quite large, we can log transform this data using the step_log() function of the recipes package.
We would also want to potentially one hot encode some of our categorical variables so that they can be used with certain algorithms. We can do this with the step_dummy() function and the one_hot = TRUE argument. Our fips variable includes a numeric code for state and county - and therefore is essentially a proxy for county. Since we already have county, we will just use it and keep the fips id as another ID variable.
We can remove the fips variable from the predictors using update_role() to make sure that the role is no longer "predictor". We can make the role anything we want actually, so we will keep it something identifiable.
We might also want to remove variables that appear to be redundant and are highly correlated with others, as we know from our exploratory data analysis that many of our variables are correlated with one another. We can do this using the step_corr() function.
It is also a good idea to remove variables with near-zero variance, which can be done with the step_nzv() function. Variables have low variance if all the values are very similar, the values are very sparse, or if they are highly imbalanced.
Examples where you might have near-zero variance variables include: ### I Struggled to find links for this… to back up my statements###
It is important to add the steps to the recipe in an order that makes sense just like with a cooking recipe.
Thus first we are going to create numeric values for our categorical variables, then we will look at correlation and near-zero variance. We don’t want to remove some of our variables, like the CMAQ and aod variables so we can make sure they are kept in the model by excluding them from those steps. If we specifically wanted to remove a predictor we could use step_rm().
simple_rec %<>%
update_role("fips", new_role = "county id") %>%
# create numeric dummy variables to encode for categorical variables
step_dummy(state, county, city, zcta, one_hot = TRUE) %>%
# identify and reomve all correlated predictors (now that they are numeric)
step_corr(all_predictors(), - CMAQ, - aod)%>%
# identify variables with near zero variance and remove
step_nzv(all_predictors(), - CMAQ, - aod)
simple_recData Recipe
Inputs:
role #variables
county id 1
id variable 1
outcome 1
predictor 47
Operations:
Dummy variables from state, county, city, zcta
Correlation filter on all_predictors, -, CMAQ, -, aod
Sparse, unbalanced variable filter on all_predictors, -, CMAQ, -, aodThe next major function of the recipes package is prep().
This function updates the recipe object based on the training data. It estimates parameters (estimating the required quantities and statistics required by the steps for the variables) for preprocessing and updates the model terms, as some of the predictors may be removed, this allows the recipe to be ready to use on other datasets. It doesn’t necessarily actually execute the preprocessing itself, however we will specify in argument for it to do this so that we can take a look at the preprocessed data.
There are some important arguments to know about: 1) training - you must supply a training data set to estimate parameters for preprocessing operations (recipe steps) - this may already be included in your recipe - as is the case for us 2) fresh - if TRUE - will retrain and estimate parameters for any previous steps that were already prepped if you add more steps to the recipe 3) verbose - if TRUE shows the progress as the steps are evaluated and the size of the preprocessed training set 4) retain - if TRUE then the preprocessed training set will be saved within the recipe (as template). This is good if you are likely to add more steps and don’t want to rerun the prep() on the previous steps. However this can make the recipe size large. This is necessary if you want to actually look at the preprocessed data.
oper 1 step dummy [training]
oper 2 step corr [training]
oper 3 step nzv [training]
The retained training set is ~ 0.26 Mb in memory.[1] "var_info" "term_info" "steps" "template"
[5] "levels" "retained" "tr_info" "orig_lvls"
[9] "last_term_info"There are also lots of useful things to checkout in the output of prep(). You can see: 1) the steps that were run
2) the variable info (var_info)
3) the model term_info 4) the new levels of the variables 5) the original levels of the variables orig_lvls
6) info about the training data set size and completeness (tr_info)
Note: You may see the prep.recipe() function in material that you read about the recipes package. This is referring to the prep() function of the recipes package.
Since we retained our preprocessed training data, we can take a look at it like by using the juice() function of the recipes package like this:
Rows: 584
Columns: 36
$ id <fct> 1003.001, 1027.0001, 1033.1002, 1055.001,…
$ value <dbl> 9.597647, 10.800000, 11.212174, 12.375394…
$ fips <fct> 1003, 1027, 1033, 1055, 1069, 1073, 1073,…
$ lat <dbl> 30.49800, 33.28126, 34.75878, 33.99375, 3…
$ lon <dbl> -87.88141, -85.80218, -87.65056, -85.9910…
$ CMAQ <dbl> 8.098836, 9.766208, 9.402679, 9.241744, 9…
$ zcta_area <dbl> 190980522, 374132430, 16716984, 154069359…
$ zcta_pop <dbl> 27829, 5103, 9042, 20045, 30217, 9010, 16…
$ imp_a500 <dbl> 0.01730104, 1.96972318, 19.17301038, 16.4…
$ imp_a15000 <dbl> 1.4386207, 0.3359198, 5.2472094, 5.161210…
$ county_area <dbl> 4117521611, 1564252280, 1534877333, 13856…
$ county_pop <dbl> 182265, 13932, 54428, 104430, 101547, 658…
$ log_dist_to_prisec <dbl> 4.648181, 7.219907, 5.760131, 5.261457, 7…
$ log_pri_length_5000 <dbl> 8.517193, 8.517193, 8.517193, 9.066563, 8…
$ log_pri_length_25000 <dbl> 11.32735, 10.12663, 10.15769, 12.01356, 1…
$ log_prisec_length_500 <dbl> 7.295356, 6.214608, 8.611945, 8.740680, 6…
$ log_prisec_length_1000 <dbl> 8.195119, 7.600902, 9.735569, 9.627898, 7…
$ log_prisec_length_5000 <dbl> 10.815042, 10.170878, 11.770407, 11.72888…
$ log_prisec_length_10000 <dbl> 11.886803, 11.405543, 12.840663, 12.76827…
$ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 4.462…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 4.678311, 3…
$ popdens_county <dbl> 44.265706, 8.906492, 35.460814, 75.367038…
$ popdens_zcta <dbl> 145.7164307, 13.6395554, 540.8870404, 130…
$ nohs <dbl> 3.3, 11.6, 7.3, 4.3, 5.8, 7.1, 2.7, 11.1,…
$ somehs <dbl> 4.9, 19.1, 15.8, 13.3, 11.6, 17.1, 6.6, 1…
$ hs <dbl> 25.1, 33.9, 30.6, 27.8, 29.8, 37.2, 30.7,…
$ somecollege <dbl> 19.7, 18.8, 20.9, 29.2, 21.4, 23.5, 25.7,…
$ associate <dbl> 8.2, 8.0, 7.6, 10.1, 7.9, 7.3, 8.0, 4.1, …
$ bachelor <dbl> 25.3, 5.5, 12.7, 10.0, 13.7, 5.9, 17.6, 7…
$ grad <dbl> 13.5, 3.1, 5.1, 5.4, 9.8, 2.0, 8.7, 2.9, …
$ pov <dbl> 6.1, 19.5, 19.0, 8.8, 15.6, 25.5, 7.3, 8.…
$ hs_orless <dbl> 33.3, 64.6, 53.7, 45.4, 47.2, 61.4, 40.0,…
$ urc2013 <dbl> 4, 6, 4, 4, 4, 1, 1, 1, 1, 1, 2, 3, 3, 3,…
$ aod <dbl> 37.363636, 34.818182, 36.000000, 43.41666…
$ state_California <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ city_Not.in.a.city <dbl> 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0,…For easy comparison sake - here is our original data: #### {.scrollable }
Rows: 876
Columns: 50
$ id <fct> 1003.001, 1027.0001, 1033.1002, 1049.1003…
$ value <dbl> 9.597647, 10.800000, 11.212174, 11.659091…
$ fips <fct> 1003, 1027, 1033, 1049, 1055, 1069, 1073,…
$ lat <dbl> 30.49800, 33.28126, 34.75878, 34.28763, 3…
$ lon <dbl> -87.88141, -85.80218, -87.65056, -85.9683…
$ state <chr> "Alabama", "Alabama", "Alabama", "Alabama…
$ county <chr> "Baldwin", "Clay", "Colbert", "DeKalb", "…
$ city <chr> "Fairhope", "Ashland", "Muscle Shoals", "…
$ CMAQ <dbl> 8.098836, 9.766208, 9.402679, 8.534772, 9…
$ zcta <fct> 36532, 36251, 35660, 35962, 35901, 36303,…
$ zcta_area <dbl> 190980522, 374132430, 16716984, 203836235…
$ zcta_pop <dbl> 27829, 5103, 9042, 8300, 20045, 30217, 90…
$ imp_a500 <dbl> 0.01730104, 1.96972318, 19.17301038, 5.78…
$ imp_a1000 <dbl> 1.4096021, 0.8531574, 11.1448962, 3.86764…
$ imp_a5000 <dbl> 3.3360118, 0.9851479, 15.1786154, 1.23114…
$ imp_a10000 <dbl> 1.9879187, 0.5208189, 9.7253870, 1.031646…
$ imp_a15000 <dbl> 1.4386207, 0.3359198, 5.2472094, 0.973044…
$ county_area <dbl> 4117521611, 1564252280, 1534877333, 20126…
$ county_pop <dbl> 182265, 13932, 54428, 71109, 104430, 1015…
$ log_dist_to_prisec <dbl> 4.648181, 7.219907, 5.760131, 3.721489, 5…
$ log_pri_length_5000 <dbl> 8.517193, 8.517193, 8.517193, 8.517193, 9…
$ log_pri_length_10000 <dbl> 9.210340, 9.210340, 9.274303, 10.409411, …
$ log_pri_length_15000 <dbl> 9.630228, 9.615805, 9.658899, 11.173626, …
$ log_pri_length_25000 <dbl> 11.32735, 10.12663, 10.15769, 11.90959, 1…
$ log_prisec_length_500 <dbl> 7.295356, 6.214608, 8.611945, 7.310155, 8…
$ log_prisec_length_1000 <dbl> 8.195119, 7.600902, 9.735569, 8.585843, 9…
$ log_prisec_length_5000 <dbl> 10.815042, 10.170878, 11.770407, 10.21420…
$ log_prisec_length_10000 <dbl> 11.88680, 11.40554, 12.84066, 11.50894, 1…
$ log_prisec_length_15000 <dbl> 12.205723, 12.042963, 13.282656, 12.35366…
$ log_prisec_length_25000 <dbl> 13.41395, 12.79980, 13.79973, 13.55979, 1…
$ log_nei_2008_pm25_sum_10000 <dbl> 0.318035438, 3.218632928, 6.573127301, 0.…
$ log_nei_2008_pm25_sum_15000 <dbl> 1.967358961, 3.218632928, 6.581917457, 3.…
$ log_nei_2008_pm25_sum_25000 <dbl> 5.067308, 3.218633, 6.875900, 4.887665, 4…
$ log_nei_2008_pm10_sum_10000 <dbl> 1.35588511, 3.31111648, 6.69187313, 0.000…
$ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 3.350…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 5.171920, 4…
$ popdens_county <dbl> 44.265706, 8.906492, 35.460814, 35.330814…
$ popdens_zcta <dbl> 145.716431, 13.639555, 540.887040, 40.718…
$ nohs <dbl> 3.3, 11.6, 7.3, 14.3, 4.3, 5.8, 7.1, 2.7,…
$ somehs <dbl> 4.9, 19.1, 15.8, 16.7, 13.3, 11.6, 17.1, …
$ hs <dbl> 25.1, 33.9, 30.6, 35.0, 27.8, 29.8, 37.2,…
$ somecollege <dbl> 19.7, 18.8, 20.9, 14.9, 29.2, 21.4, 23.5,…
$ associate <dbl> 8.2, 8.0, 7.6, 5.5, 10.1, 7.9, 7.3, 8.0, …
$ bachelor <dbl> 25.3, 5.5, 12.7, 7.9, 10.0, 13.7, 5.9, 17…
$ grad <dbl> 13.5, 3.1, 5.1, 5.8, 5.4, 9.8, 2.0, 8.7, …
$ pov <dbl> 6.1, 19.5, 19.0, 13.8, 8.8, 15.6, 25.5, 7…
$ hs_orless <dbl> 33.3, 64.6, 53.7, 66.0, 45.4, 47.2, 61.4,…
$ urc2013 <dbl> 4, 6, 4, 6, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ urc2006 <dbl> 5, 6, 4, 5, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2,…
$ aod <dbl> 37.36364, 34.81818, 36.00000, 33.08333, 4…Notice how we only have 36 variables now instead of 50! Two of these are our ID variables (fips and the actual monitor ID (id)) and one is our outcome (value). Thus we only have 33 predictors now. We can also see that variables that we no longer have any categorical variables. Variables like state are gone and only state_California remains as it was the only state identity to have nonzero variance. We can see that California had the largest number of monitors compared to the other states. We can also see that there were more monitors listed as "Not in a city" than any city.
# A tibble: 49 x 2
state n
<chr> <int>
1 Alabama 24
2 Arizona 17
3 Arkansas 16
4 California 85
5 Colorado 15
6 Connecticut 14
7 Delaware 7
8 District Of Columbia 3
9 Florida 29
10 Georgia 28
# … with 39 more rows# A tibble: 607 x 2
city n
<chr> <int>
1 Aberdeen 1
2 Akron 2
3 Albany 3
4 Albuquerque 2
5 Alexandria 1
6 Allen Park 1
7 Altamont 1
8 Alton 1
9 Amarillo 1
10 Anadarko 1
# … with 597 more rowsNote: Recall that you must specify retain = TRUE argument of the prep() function to use juice().
Accroding to the tidymodels documentation:
bake()takes a trained recipe and applies the operations to a data set to create a design matrix. for example: it applies the centering to new data sets using these means used to create the recipe
NOTE this next section could be removed if it is confusing… and we would therefore update the orginal simple_rec recipe. But it shows what I had difficulty with - the new levels in testing data..
If you wanted to look at the preprocessed testing data you would use the bake() function of the recipes package. (You generally want to leave your testing data alone, but it is good to look for issues like the introduction of NA values).
# Scroll therough the output!
baked_test_pm <- recipes::bake(prepped_rec, new_data = test_pm)
glimpse(baked_test_pm )Rows: 292
Columns: 36
$ id <fct> 1049.1003, 1073.101, 1073.2006, 1089.0014…
$ value <dbl> 11.659091, 13.114545, 12.228125, 12.23294…
$ fips <fct> 1049, 1073, 1073, 1089, 1103, 1121, 4013,…
$ lat <dbl> 34.28763, 33.54528, 33.38639, 34.68767, 3…
$ lon <dbl> -85.96830, -86.54917, -86.81667, -86.5863…
$ CMAQ <dbl> 8.534772, 9.303766, 10.235612, 9.343611, …
$ zcta_area <dbl> 203836235, 148994881, 56063756, 46963946,…
$ zcta_pop <dbl> 8300, 14212, 32390, 21297, 30545, 7713, 5…
$ imp_a500 <dbl> 5.78200692, 0.06055363, 42.42820069, 23.2…
$ imp_a15000 <dbl> 0.9730444, 2.9956557, 12.7487614, 10.3555…
$ county_area <dbl> 2012662359, 2878192209, 2878192209, 20761…
$ county_pop <dbl> 71109, 658466, 658466, 334811, 119490, 82…
$ log_dist_to_prisec <dbl> 3.721489, 7.301545, 4.721755, 4.659519, 6…
$ log_pri_length_5000 <dbl> 8.517193, 9.683336, 10.737240, 8.517193, …
$ log_pri_length_25000 <dbl> 11.90959, 12.53777, 12.99669, 11.47391, 1…
$ log_prisec_length_500 <dbl> 7.310155, 6.214608, 7.528913, 8.760549, 6…
$ log_prisec_length_1000 <dbl> 8.585843, 7.600902, 9.342290, 9.543183, 8…
$ log_prisec_length_5000 <dbl> 10.214200, 11.262645, 11.713190, 11.48606…
$ log_prisec_length_10000 <dbl> 11.50894, 12.14101, 12.53899, 12.68440, 1…
$ log_nei_2008_pm10_sum_15000 <dbl> 3.3500444, 6.6241114, 5.8268686, 3.861625…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.1719202, 7.5490587, 8.8205542, 5.219092…
$ popdens_county <dbl> 35.330814, 228.777633, 228.777633, 161.26…
$ popdens_zcta <dbl> 40.718962, 95.385827, 577.735106, 453.475…
$ nohs <dbl> 14.3, 7.2, 0.8, 1.2, 4.8, 16.7, 19.1, 6.4…
$ somehs <dbl> 16.7, 12.2, 2.6, 3.1, 7.8, 33.3, 15.6, 9.…
$ hs <dbl> 35.0, 32.2, 12.9, 15.1, 28.7, 37.5, 26.5,…
$ somecollege <dbl> 14.9, 19.0, 17.9, 20.5, 25.0, 12.5, 18.0,…
$ associate <dbl> 5.5, 6.8, 5.2, 6.5, 7.5, 0.0, 6.0, 8.8, 3…
$ bachelor <dbl> 7.9, 14.8, 35.5, 30.4, 18.2, 0.0, 10.6, 1…
$ grad <dbl> 5.8, 7.7, 25.2, 23.3, 8.0, 0.0, 4.1, 5.7,…
$ pov <dbl> 13.8, 10.5, 2.1, 5.2, 8.3, 18.8, 21.4, 14…
$ hs_orless <dbl> 66.0, 51.6, 16.3, 19.4, 41.3, 87.5, 61.2,…
$ urc2013 <dbl> 6, 1, 1, 3, 4, 5, 1, 2, 5, 4, 4, 6, 6, 1,…
$ aod <dbl> 33.08333, 42.45455, 44.25000, 42.41667, 4…
$ state_California <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,…
$ city_Not.in.a.city <dbl> NA, NA, NA, NA, NA, NA, 0, NA, NA, NA, NA…Notice that our city_Not.in.a.city variable seems to be NA values. Why might that be?
Ah! Perphas it is because some of our levels were not previously seen in the training set!
Let’s take a look using the set operations of the dplyr package. We can take a look at cities that were different between the test and training set.
traincities <- train_pm %>% distinct(city)
testcities <- test_pm %>% distinct(city)
#get the number of cities that were different
dim(dplyr::setdiff(traincities, testcities))[1] 376 1[1] 51 1Indeed, there are lots of different cities in our test data that are not in our training data!
Maybe remove this?: Thus we need to update our original recipe to include a very important step function called step_novel() this helps in cases like this were there are new factors in our testing set that were not in our training set. It is a good idea to include this in most of your recipes where you have a categorical variables with many distinct values. This step needs to come before we create dummy variables. However, we are also creating a dummy variable from this, which still results in a problem.
Let’s modify the city variable to be values of in a city or not in a city using the if_else() function of dplyr. Alternatively you could create a custom step function to do this and add the step function to your recipe, but that is beyond the scope of this case study.
We need to create a new recipe to move forward, as the levels of our variables are established then. We would also potentially have this issue for state and county. So let’s also do a similar thing for state. The county variables appears to get dropped due to either correlation or near zero variance. It is likely due to near zero variance becuase this is the more granular of these geographic categorical variables and likely sparse.
train_pm[["city"]] <- if_else(
train_pm[["city"]] == "Not in a city",
true = "Not in a city", false = "In a city")
test_pm[["city"]] <- if_else(
test_pm[["city"]] == "Not in a city",
true = "Not in a city", false = "In a city")
train_pm[["state"]] <- if_else(
train_pm[["state"]] == "California",
true = "California", false = "Not California")
test_pm[["state"]] <- if_else(
test_pm[["state"]] == "California",
true = "California", false = "Not California")
novel_rec <-recipe(train_pm) %>%
update_role(everything(), new_role = "predictor")%>%
update_role(value, new_role = "outcome")%>%
update_role(id, new_role = "id variable")%>%
update_role("fips", new_role = "county id")%>%
# create numeric dummy variables to encode for categorical variables
step_dummy(state, county, city, zcta, one_hot = TRUE) %>%
# identify and reomve all correlated predictors (now that they are numeric)
step_corr(all_numeric())%>%
# identify variables with near zero variance and remove
step_nzv(all_numeric()) # Now let’s retrain our training data and try baking our test data:
oper 1 step dummy [training]
oper 2 step corr [training]
oper 3 step nzv [training]
The retained training set is ~ 0.26 Mb in memory.Rows: 584
Columns: 37
$ id <fct> 1003.001, 1027.0001, 1033.1002, 1055.001,…
$ value <dbl> 9.597647, 10.800000, 11.212174, 12.375394…
$ fips <fct> 1003, 1027, 1033, 1055, 1069, 1073, 1073,…
$ lat <dbl> 30.49800, 33.28126, 34.75878, 33.99375, 3…
$ lon <dbl> -87.88141, -85.80218, -87.65056, -85.9910…
$ CMAQ <dbl> 8.098836, 9.766208, 9.402679, 9.241744, 9…
$ zcta_area <dbl> 190980522, 374132430, 16716984, 154069359…
$ zcta_pop <dbl> 27829, 5103, 9042, 20045, 30217, 9010, 16…
$ imp_a500 <dbl> 0.01730104, 1.96972318, 19.17301038, 16.4…
$ imp_a15000 <dbl> 1.4386207, 0.3359198, 5.2472094, 5.161210…
$ county_area <dbl> 4117521611, 1564252280, 1534877333, 13856…
$ county_pop <dbl> 182265, 13932, 54428, 104430, 101547, 658…
$ log_dist_to_prisec <dbl> 4.648181, 7.219907, 5.760131, 5.261457, 7…
$ log_pri_length_5000 <dbl> 8.517193, 8.517193, 8.517193, 9.066563, 8…
$ log_pri_length_25000 <dbl> 11.32735, 10.12663, 10.15769, 12.01356, 1…
$ log_prisec_length_500 <dbl> 7.295356, 6.214608, 8.611945, 8.740680, 6…
$ log_prisec_length_1000 <dbl> 8.195119, 7.600902, 9.735569, 9.627898, 7…
$ log_prisec_length_5000 <dbl> 10.815042, 10.170878, 11.770407, 11.72888…
$ log_prisec_length_10000 <dbl> 11.886803, 11.405543, 12.840663, 12.76827…
$ log_prisec_length_25000 <dbl> 13.41395, 12.79980, 13.79973, 13.70026, 1…
$ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 4.462…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 4.678311, 3…
$ popdens_county <dbl> 44.265706, 8.906492, 35.460814, 75.367038…
$ popdens_zcta <dbl> 145.7164307, 13.6395554, 540.8870404, 130…
$ nohs <dbl> 3.3, 11.6, 7.3, 4.3, 5.8, 7.1, 2.7, 11.1,…
$ somehs <dbl> 4.9, 19.1, 15.8, 13.3, 11.6, 17.1, 6.6, 1…
$ hs <dbl> 25.1, 33.9, 30.6, 27.8, 29.8, 37.2, 30.7,…
$ somecollege <dbl> 19.7, 18.8, 20.9, 29.2, 21.4, 23.5, 25.7,…
$ associate <dbl> 8.2, 8.0, 7.6, 10.1, 7.9, 7.3, 8.0, 4.1, …
$ bachelor <dbl> 25.3, 5.5, 12.7, 10.0, 13.7, 5.9, 17.6, 7…
$ grad <dbl> 13.5, 3.1, 5.1, 5.4, 9.8, 2.0, 8.7, 2.9, …
$ pov <dbl> 6.1, 19.5, 19.0, 8.8, 15.6, 25.5, 7.3, 8.…
$ hs_orless <dbl> 33.3, 64.6, 53.7, 45.4, 47.2, 61.4, 40.0,…
$ urc2013 <dbl> 4, 6, 4, 4, 4, 1, 1, 1, 1, 1, 2, 3, 3, 3,…
$ aod <dbl> 37.363636, 34.818182, 36.000000, 43.41666…
$ state_Not.California <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ city_Not.in.a.city <dbl> 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0,…Notice, it looks like we gained the log_prisec_length_25000 back with this recipe using the data with our changes to state and city.
Rows: 292
Columns: 37
$ id <fct> 1049.1003, 1073.101, 1073.2006, 1089.0014…
$ value <dbl> 11.659091, 13.114545, 12.228125, 12.23294…
$ fips <fct> 1049, 1073, 1073, 1089, 1103, 1121, 4013,…
$ lat <dbl> 34.28763, 33.54528, 33.38639, 34.68767, 3…
$ lon <dbl> -85.96830, -86.54917, -86.81667, -86.5863…
$ CMAQ <dbl> 8.534772, 9.303766, 10.235612, 9.343611, …
$ zcta_area <dbl> 203836235, 148994881, 56063756, 46963946,…
$ zcta_pop <dbl> 8300, 14212, 32390, 21297, 30545, 7713, 5…
$ imp_a500 <dbl> 5.78200692, 0.06055363, 42.42820069, 23.2…
$ imp_a15000 <dbl> 0.9730444, 2.9956557, 12.7487614, 10.3555…
$ county_area <dbl> 2012662359, 2878192209, 2878192209, 20761…
$ county_pop <dbl> 71109, 658466, 658466, 334811, 119490, 82…
$ log_dist_to_prisec <dbl> 3.721489, 7.301545, 4.721755, 4.659519, 6…
$ log_pri_length_5000 <dbl> 8.517193, 9.683336, 10.737240, 8.517193, …
$ log_pri_length_25000 <dbl> 11.90959, 12.53777, 12.99669, 11.47391, 1…
$ log_prisec_length_500 <dbl> 7.310155, 6.214608, 7.528913, 8.760549, 6…
$ log_prisec_length_1000 <dbl> 8.585843, 7.600902, 9.342290, 9.543183, 8…
$ log_prisec_length_5000 <dbl> 10.214200, 11.262645, 11.713190, 11.48606…
$ log_prisec_length_10000 <dbl> 11.50894, 12.14101, 12.53899, 12.68440, 1…
$ log_prisec_length_25000 <dbl> 13.55979, 14.08915, 14.27363, 13.87170, 1…
$ log_nei_2008_pm10_sum_15000 <dbl> 3.3500444, 6.6241114, 5.8268686, 3.861625…
$ log_nei_2008_pm10_sum_25000 <dbl> 5.1719202, 7.5490587, 8.8205542, 5.219092…
$ popdens_county <dbl> 35.330814, 228.777633, 228.777633, 161.26…
$ popdens_zcta <dbl> 40.718962, 95.385827, 577.735106, 453.475…
$ nohs <dbl> 14.3, 7.2, 0.8, 1.2, 4.8, 16.7, 19.1, 6.4…
$ somehs <dbl> 16.7, 12.2, 2.6, 3.1, 7.8, 33.3, 15.6, 9.…
$ hs <dbl> 35.0, 32.2, 12.9, 15.1, 28.7, 37.5, 26.5,…
$ somecollege <dbl> 14.9, 19.0, 17.9, 20.5, 25.0, 12.5, 18.0,…
$ associate <dbl> 5.5, 6.8, 5.2, 6.5, 7.5, 0.0, 6.0, 8.8, 3…
$ bachelor <dbl> 7.9, 14.8, 35.5, 30.4, 18.2, 0.0, 10.6, 1…
$ grad <dbl> 5.8, 7.7, 25.2, 23.3, 8.0, 0.0, 4.1, 5.7,…
$ pov <dbl> 13.8, 10.5, 2.1, 5.2, 8.3, 18.8, 21.4, 14…
$ hs_orless <dbl> 66.0, 51.6, 16.3, 19.4, 41.3, 87.5, 61.2,…
$ urc2013 <dbl> 6, 1, 1, 3, 4, 5, 1, 2, 5, 4, 4, 6, 6, 1,…
$ aod <dbl> 33.08333, 42.45455, 44.25000, 42.41667, 4…
$ state_Not.California <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,…
$ city_Not.in.a.city <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…Great now we no longer have NA values! :)
Note: if you use the skip option for some of the preprocessing steps, be careful. juice() will show all of the results ignoring skip = TRUE. bake() will not necessarily conduct these steps on the new data.
So far we have used rsample to split the data and recipes to assign variable and to specify and prep our preprocessing (as well as to optionally extract the preprocessed data).
We will now use the parsnip package (which is similar to the previous caret package - and hence why it is named after the vegetable) to specify our model.
There are four aspects to define about our model:
1) the type of model (using specific funtions in parsnip like rand_forest(), logistic_reg() etc.)
2) the mode of learning - classification or regression (using the set_mode() function)
3) the package or engine that we will use to implement the type of model selected (using the set_engine() function)
4) any arguments necessary for the model/package selected (using the set_args()function - for example the mtry = argument for random forest which is the number of variables to be used as options for splitting at each tree node)
We are going to start our analysis with a linear regression but we will demonstrate how we can try different models.
The first thing we do is define what type of model we would like to use. See here for modeling [options]in parsnip.
Linear Regression Model Specification (regression)OK. So far all we have told parsnip is we want to use a linear regression… Let’s tell parsnip more about what we want.
We would like to use the ordinary least squares method to fit our linear regression. So we will tell parsnip that we want to use the lm package to implement our linear regression (there are many options actually- such as rstan glmnet, keras, and sparklyr). We will do so by using the set_engine() function of the parsnip package.
Linear Regression Model Specification (regression)
Computational engine: lm In some cases some packages can do either classification or prediction, so it is a good idea to specify which mode you intend to perform. You can do this with the set_mode() function of the parsnip package, by using either set_mode("classification") or set_mode("regression").
Linear Regression Model Specification (regression)
Computational engine: lm workflows and parsnipThere are two w To fit our model we can use the parsnip package and then assess our fit using the yardstick package.
However a newer package called workflows allows us to keep track of both our preprocessing steps and our model specification. It also allows us to implement fancier optimizations in an automated way and it is currently being developed to also handle post-processing operations, so it is good to learn about it!
So we will now create a workflow with the recipe (our preprocessing specifications) that we made and the model that we just specified.
First we use the workflow() function of the workflows package to create a workflow.
Then we add our recipe with the add_recipe() function and we add our model with the add_model() function of the workflows package.
Note: We do not need to actually prep our recipe before using workflows!
PM_wflow <-workflows::workflow() %>%
workflows::add_recipe(novel_rec) %>%
workflows::add_model(lm_PM_model)
PM_wflow══ Workflow ═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: linear_reg()
── Preprocessor ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
3 Recipe Steps
● step_dummy()
● step_corr()
● step_nzv()
── Model ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Linear Regression Model Specification (regression)
Computational engine: lm Ah, nice. Notice how it tells us about both our preprocessing steps and our model specifications.
Now we can prepare the recipe (estimate the parameters) and fit the model to our training data all at once. Printing the output we can see the coefficients of the model.
══ Workflow [trained] ═════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: linear_reg()
── Preprocessor ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
3 Recipe Steps
● step_dummy()
● step_corr()
● step_nzv()
── Model ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Call:
stats::lm(formula = formula, data = data)
Coefficients:
(Intercept) lat
2.265e+02 3.639e-02
lon CMAQ
2.579e-02 2.847e-01
zcta_area zcta_pop
3.638e-10 7.880e-06
imp_a500 imp_a15000
7.453e-03 -1.140e-03
county_area county_pop
-2.116e-11 -2.156e-07
log_dist_to_prisec log_pri_length_5000
4.064e-02 -1.842e-01
log_pri_length_25000 log_prisec_length_500
7.936e-03 2.572e-01
log_prisec_length_1000 log_prisec_length_5000
-2.288e-02 4.743e-01
log_prisec_length_10000 log_prisec_length_25000
-1.410e-01 4.658e-01
log_nei_2008_pm10_sum_15000 log_nei_2008_pm10_sum_25000
1.088e-01 5.255e-02
popdens_county popdens_zcta
-4.114e-05 -1.816e-05
nohs somehs
-2.234e+00 -2.270e+00
hs somecollege
-2.271e+00 -2.274e+00
associate bachelor
-2.272e+00 -2.277e+00
grad pov
-2.284e+00 7.001e-03
hs_orless urc2013
NA 2.153e-01
aod state_Not.California
2.555e-02 -3.445e+00
city_Not.in.a.city
3.550e-01 Otherwise we could have done this without the workflows package. Notice here we will used the processed training data (juiced_train) as opposed to the raw training data that we used with the workflow we created with workflows.
Remember that in this case, we need to write your model again! Recall that id and fips are ID variables and that values is our outcome of interest (the pm air pollution measure at each monitor).
broomThe broom package allows for an easy/tidy way to look at the fitted model:
tidy() grabs the coefficients from the model
glance() summarizes the model fit and gives us an idea about how well the model might perform augment() gives a 150 row observation level summary of the data and fit
These broom functions currently only work with parsnip objects not raw workflows objects. To use the tidy() function with workflows we need to first use the pull_workflow_fit() function.
# A tibble: 34 x 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 state_Not.California -3.44 0.436 -7.91 1.45e-14
2 CMAQ 0.285 0.0430 6.61 8.90e-11
3 aod 0.0256 0.00575 4.45 1.06e- 5
4 lon 0.0258 0.00998 2.58 1.00e- 2
5 county_pop -0.000000216 0.0000000934 -2.31 2.14e- 2
6 urc2013 0.215 0.101 2.13 3.35e- 2
7 grad -2.28 1.20 -1.90 5.78e- 2
8 bachelor -2.28 1.20 -1.90 5.84e- 2
9 somecollege -2.27 1.20 -1.89 5.87e- 2
10 associate -2.27 1.20 -1.89 5.90e- 2
# … with 24 more rows# A tibble: 1 x 11
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1 0.433 0.399 2.08 12.7 1.02e-48 34 -1240. 2550. 2703.
# … with 2 more variables: deviance <dbl>, df.residual <int># A tibble: 584 x 42
value lat lon CMAQ zcta_area zcta_pop imp_a500 imp_a15000 county_area
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 9.60 30.5 -87.9 8.10 190980522 27829 0.0173 1.44 4117521611
2 10.8 33.3 -85.8 9.77 374132430 5103 1.97 0.336 1564252280
3 11.2 34.8 -87.7 9.40 16716984 9042 19.2 5.25 1534877333
4 12.4 34.0 -86.0 9.24 154069359 20045 16.5 5.16 1385618994
5 10.5 31.2 -85.4 9.12 162685124 30217 19.1 4.74 1501737720
6 15.6 33.6 -86.8 10.2 26929603 9010 41.8 17.5 2878192209
7 12.4 33.3 -87.0 10.2 166239542 16140 1.70 4.30 2878192209
8 11.1 33.5 -87.3 8.16 385566685 3699 0 0.162 3423328940
9 14.6 33.5 -86.9 10.2 10636977 11458 43.6 15.6 2878192209
10 12.0 33.7 -86.7 9.30 150661846 21725 1.48 4.25 2878192209
# … with 574 more rows, and 33 more variables: county_pop <dbl>,
# log_dist_to_prisec <dbl>, log_pri_length_5000 <dbl>,
# log_pri_length_25000 <dbl>, log_prisec_length_500 <dbl>,
# log_prisec_length_1000 <dbl>, log_prisec_length_5000 <dbl>,
# log_prisec_length_10000 <dbl>, log_prisec_length_25000 <dbl>,
# log_nei_2008_pm10_sum_15000 <dbl>, log_nei_2008_pm10_sum_25000 <dbl>,
# popdens_county <dbl>, popdens_zcta <dbl>, nohs <dbl>, somehs <dbl>,
# hs <dbl>, somecollege <dbl>, associate <dbl>, bachelor <dbl>, grad <dbl>,
# pov <dbl>, hs_orless <dbl>, urc2013 <dbl>, aod <dbl>,
# state_Not.California <dbl>, city_Not.in.a.city <dbl>, .fitted <dbl>,
# .se.fit <dbl>, .resid <dbl>, .hat <dbl>, .sigma <dbl>, .cooksd <dbl>,
# .std.resid <dbl>wflowoutput<-PM_wflow_fit %>%
pull_workflow_fit() %>%
broom::tidy()
#The output is identical using workflows to fit the model or just parsnip
identical(tidy(PM_fit), wflowoutput)[1] TRUEOK, so we have fit our model on our training data, which means we have created a model to predict values of air pollution based on the predictors that we have included. Yay!
Let’s take a look at how well our model fit our training data:
##using the parsnip version
#can grab the fitted values simply like this:
parsnip_fitted_values<-fitted(PM_fit[["fit"]])
parsnip_fitted_values 1 2 3 4 5 6 7 8
9.461664 10.429189 11.795351 11.139746 10.863402 11.091857 10.073411 8.189021
9 10 11 12 13 14 15 16
11.517888 10.618367 9.557499 10.218323 9.865608 11.011802 12.139040 10.202025
17 18 19 20 21 22 23 24
10.517763 9.548571 6.837646 7.472453 7.018230 10.126795 10.133236 9.582305
25 26 27 28 29 30 31 32
9.702583 6.862089 7.005665 8.477788 8.892971 9.244236 11.417965 10.464960
33 34 35 36 37 38 39 40
9.652665 9.943594 11.435373 10.090206 10.304301 11.188076 11.193689 10.767763
41 42 43 44 45 46 47 48
10.722817 9.949272 10.521367 9.976252 11.955651 11.674338 13.902418 13.582229
49 50 51 52 53 54 55 56
14.713622 11.219505 11.320158 15.169192 8.682176 13.357477 11.166948 14.162085
57 58 59 60 61 62 63 64
13.128209 10.867659 12.557864 11.404720 14.609938 10.003168 11.917995 9.886651
65 66 67 68 69 70 71 72
11.161819 12.326977 12.722475 11.439546 11.380029 14.615337 10.945608 12.754387
73 74 75 76 77 78 79 80
11.464256 13.050833 11.162822 14.092701 10.025276 12.181293 12.573405 12.850499
81 82 83 84 85 86 87 88
12.523434 13.398889 8.867379 12.250365 15.385913 10.726820 12.320977 12.282267
89 90 91 92 93 94 95 96
10.903510 13.504498 10.678776 11.367829 14.267153 11.959658 14.860756 12.245437
97 98 99 100 101 102 103 104
11.009600 12.303933 10.376440 9.254959 8.458964 10.797185 9.615059 8.319766
105 106 107 108 109 110 111 112
6.584026 8.480982 7.889599 8.520672 9.507922 9.460726 12.291791 10.315367
113 114 115 116 117 118 119 120
9.899759 10.270368 9.531778 8.476645 10.506159 10.457589 11.548915 12.211470
121 122 123 124 125 126 127 128
12.754005 11.760960 11.527420 13.358326 12.970527 11.450112 9.662891 8.860986
129 130 131 132 133 134 135 136
9.630399 9.107099 9.336214 10.377070 10.913731 10.012413 11.655663 9.197286
137 138 139 140 141 142 143 144
9.895577 8.992575 11.062182 10.928292 11.173204 9.290713 9.462250 9.815623
145 146 147 148 149 150 151 152
10.567132 10.041853 12.438193 12.837043 11.155833 11.068409 11.568628 10.646408
153 154 155 156 157 158 159 160
11.120305 10.674787 11.342914 11.600863 9.872202 12.933636 12.330424 10.674265
161 162 163 164 165 166 167 168
10.692636 8.591527 8.483559 8.277465 9.219110 7.999004 7.325638 10.668789
169 170 171 172 173 174 175 176
10.442171 13.278721 12.987068 12.609307 12.139812 13.311952 9.560588 11.231509
177 178 179 180 181 182 183 184
9.614572 11.388626 11.027188 10.701644 10.408321 11.281993 11.952935 12.314095
185 186 187 188 189 190 191 192
11.343060 12.301626 11.670473 11.538465 11.450721 12.583606 9.908812 11.957886
193 194 195 196 197 198 199 200
12.476480 11.356784 11.408551 11.386678 11.371265 11.869010 11.386166 10.716040
201 202 203 204 205 206 207 208
13.547182 13.430563 14.488555 13.382721 11.721882 13.138956 11.617227 12.919960
209 210 211 212 213 214 215 216
11.610622 11.234236 12.441517 11.565354 11.775386 11.870380 11.612343 10.513345
217 218 219 220 221 222 223 224
11.332066 11.356102 8.622875 9.342198 10.532866 11.075768 10.814015 9.148910
225 226 227 228 229 230 231 232
10.259892 8.851762 10.150785 11.702025 11.247041 9.448320 8.715848 10.465157
233 234 235 236 237 238 239 240
9.063738 8.512195 9.359375 8.694810 12.250888 10.950829 11.172992 11.113227
241 242 243 244 245 246 247 248
12.539577 11.130235 11.520853 13.270299 12.445247 11.641586 11.084325 11.681937
249 250 251 252 253 254 255 256
12.903454 11.675062 11.868743 11.887980 12.142425 11.125280 10.206552 13.083514
257 258 259 260 261 262 263 264
12.553520 13.232212 11.590232 11.070216 11.072157 11.721994 10.595329 14.228343
265 266 267 268 269 270 271 272
13.651194 10.111261 12.956021 13.017707 10.712920 13.277355 11.914351 11.578296
273 274 275 276 277 278 279 280
12.601671 13.808564 13.137512 11.706520 11.860984 9.304048 10.849169 10.160520
281 282 283 284 285 286 287 288
10.957044 10.853018 11.595010 11.208375 11.222850 10.646720 10.875621 10.875865
289 290 291 292 293 294 295 296
12.139867 9.344793 7.829627 7.419011 10.276070 8.595271 11.984527 10.025066
297 298 299 300 301 302 303 304
11.658014 10.844432 13.668283 13.877468 11.842378 12.609642 12.315624 7.550419
305 306 307 308 309 310 311 312
10.543817 10.140751 10.640678 9.986984 10.672587 12.808831 8.608027 8.762374
313 314 315 316 317 318 319 320
9.800301 8.990358 10.913175 10.986842 9.848777 10.184492 10.730669 8.925857
321 322 323 324 325 326 327 328
9.810568 11.051639 12.301691 13.244583 12.143078 7.420562 7.181852 8.115063
329 330 331 332 333 334 335 336
7.557550 7.598764 7.963658 6.033631 8.174960 7.009403 6.547324 6.721532
337 338 339 340 341 342 343 344
10.495751 10.127753 8.447220 8.955561 9.111061 6.229223 7.721007 8.702168
345 346 347 348 349 350 351 352
9.796073 10.735891 10.674564 9.993831 9.387035 11.404517 12.718761 12.490109
353 354 355 356 357 358 359 360
12.490096 12.868844 14.159822 11.862943 12.490662 12.814318 13.292919 11.342429
361 362 363 364 365 366 367 368
11.790078 13.543314 12.475061 11.439849 9.501710 9.938767 8.662747 9.361561
369 370 371 372 373 374 375 376
7.333849 7.619211 8.424590 8.182639 8.244907 11.421981 12.598988 12.766756
377 378 379 380 381 382 383 384
10.004449 11.846089 11.484665 8.502844 9.985085 14.093239 11.022401 10.343070
385 386 387 388 389 390 391 392
10.870999 11.580658 8.164514 9.816118 13.810603 10.765304 10.679352 8.943409
393 394 395 396 397 398 399 400
11.394455 10.988983 11.911609 11.169336 10.926602 11.106484 10.975384 10.570735
401 402 403 404 405 406 407 408
10.800890 11.216585 11.003865 12.058352 8.979768 10.417642 10.840787 8.564483
409 410 411 412 413 414 415 416
10.468748 7.722598 9.024726 8.627277 8.712337 12.306801 11.259834 12.135047
417 418 419 420 421 422 423 424
12.909887 13.900961 14.613681 14.659878 14.516719 11.834130 12.835139 11.524950
425 426 427 428 429 430 431 432
11.205715 12.690535 12.366608 12.257143 11.554346 11.571765 10.268979 13.831592
433 434 435 436 437 438 439 440
12.488541 12.274712 11.792411 12.159000 11.286455 12.398744 12.720250 11.839790
441 442 443 444 445 446 447 448
12.042530 10.616712 11.592961 8.680015 10.002905 10.098331 9.303447 8.025186
449 450 451 452 453 454 455 456
8.160942 7.701500 7.573096 6.440509 8.413890 7.573817 8.654901 6.527707
457 458 459 460 461 462 463 464
9.316892 9.239795 7.577079 7.234717 7.744910 10.396131 11.349235 10.531142
465 466 467 468 469 470 471 472
11.286622 11.324207 11.904075 11.984744 11.254344 10.087881 12.491983 12.727448
473 474 475 476 477 478 479 480
11.023725 9.843285 12.532214 10.909423 11.556938 11.246725 13.678810 10.995575
481 482 483 484 485 486 487 488
13.406587 12.947436 11.536939 10.519024 10.614975 10.691272 12.606993 11.966835
489 490 491 492 493 494 495 496
11.220192 9.923407 11.012463 9.424555 10.077508 10.808538 10.687251 11.438914
497 498 499 500 501 502 503 504
12.408781 10.434905 8.167398 7.968639 7.492743 7.971856 7.794390 8.631370
505 506 507 508 509 510 511 512
7.279254 7.833077 10.330354 10.925965 10.909906 8.503572 12.117403 10.667929
513 514 515 516 517 518 519 520
10.129061 10.550327 9.918316 11.522068 11.296737 11.553654 10.476981 11.941762
521 522 523 524 525 526 527 528
10.578826 11.080807 9.211676 10.323909 9.621231 8.335038 8.188955 9.082492
529 530 531 532 533 534 535 536
8.075345 9.420944 8.314572 9.247623 8.538591 9.859266 7.647124 9.902155
537 538 539 540 541 542 543 544
8.546524 9.920558 11.604894 11.918312 12.416602 10.819737 11.466657 11.179962
545 546 547 548 549 550 551 552
11.665760 9.817793 14.172912 10.192052 11.355575 13.772991 8.847900 7.970775
553 554 555 556 557 558 559 560
7.460673 8.349559 8.135941 11.447727 11.618942 11.936942 10.918982 11.041702
561 562 563 564 565 566 567 568
9.949377 11.499303 10.904615 11.689807 11.747444 11.380585 11.009586 10.850464
569 570 571 572 573 574 575 576
11.602371 11.551376 12.485626 11.270907 10.170153 10.619552 9.784335 8.033726
577 578 579 580 581 582 583 584
10.810373 8.993775 5.743434 8.959191 8.089329 6.061699 8.339742 6.931294 #can also get the values using the augment function
parsnip_fitted_values <- augment(PM_fit[["fit"]], data = juiced_train) %>%
select(value, .fitted:.std.resid)
parsnip_fitted_values# A tibble: 584 x 8
value .fitted .se.fit .resid .hat .sigma .cooksd .std.resid
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 9.60 9.46 0.375 0.136 0.0324 2.09 0.00000433 0.0663
2 10.8 10.4 0.383 0.371 0.0338 2.09 0.0000338 0.181
3 11.2 11.8 0.404 -0.583 0.0376 2.09 0.0000936 -0.285
4 12.4 11.1 0.388 1.24 0.0346 2.08 0.000384 0.604
5 10.5 10.9 0.426 -0.355 0.0418 2.09 0.0000388 -0.174
6 15.6 11.1 0.379 4.50 0.0332 2.08 0.00486 2.20
7 12.4 10.1 0.459 2.33 0.0485 2.08 0.00196 1.14
8 11.1 8.19 0.777 2.91 0.139 2.08 0.0108 1.51
9 14.6 11.5 0.378 3.03 0.0329 2.08 0.00219 1.48
10 12.0 10.6 0.452 1.33 0.0470 2.08 0.000623 0.656
# … with 574 more rows##using the workflows version
wf_fit <-PM_wflow_fit %>%
pull_workflow_fit()
#can grab the fitted values simply like this:
wf_fitted_values<-fitted(wf_fit[["fit"]])
wf_fitted_values 1 2 3 4 5 6 7 8
9.461664 10.429189 11.795351 11.139746 10.863402 11.091857 10.073411 8.189021
9 10 11 12 13 14 15 16
11.517888 10.618367 9.557499 10.218323 9.865608 11.011802 12.139040 10.202025
17 18 19 20 21 22 23 24
10.517763 9.548571 6.837646 7.472453 7.018230 10.126795 10.133236 9.582305
25 26 27 28 29 30 31 32
9.702583 6.862089 7.005665 8.477788 8.892971 9.244236 11.417965 10.464960
33 34 35 36 37 38 39 40
9.652665 9.943594 11.435373 10.090206 10.304301 11.188076 11.193689 10.767763
41 42 43 44 45 46 47 48
10.722817 9.949272 10.521367 9.976252 11.955651 11.674338 13.902418 13.582229
49 50 51 52 53 54 55 56
14.713622 11.219505 11.320158 15.169192 8.682176 13.357477 11.166948 14.162085
57 58 59 60 61 62 63 64
13.128209 10.867659 12.557864 11.404720 14.609938 10.003168 11.917995 9.886651
65 66 67 68 69 70 71 72
11.161819 12.326977 12.722475 11.439546 11.380029 14.615337 10.945608 12.754387
73 74 75 76 77 78 79 80
11.464256 13.050833 11.162822 14.092701 10.025276 12.181293 12.573405 12.850499
81 82 83 84 85 86 87 88
12.523434 13.398889 8.867379 12.250365 15.385913 10.726820 12.320977 12.282267
89 90 91 92 93 94 95 96
10.903510 13.504498 10.678776 11.367829 14.267153 11.959658 14.860756 12.245437
97 98 99 100 101 102 103 104
11.009600 12.303933 10.376440 9.254959 8.458964 10.797185 9.615059 8.319766
105 106 107 108 109 110 111 112
6.584026 8.480982 7.889599 8.520672 9.507922 9.460726 12.291791 10.315367
113 114 115 116 117 118 119 120
9.899759 10.270368 9.531778 8.476645 10.506159 10.457589 11.548915 12.211470
121 122 123 124 125 126 127 128
12.754005 11.760960 11.527420 13.358326 12.970527 11.450112 9.662891 8.860986
129 130 131 132 133 134 135 136
9.630399 9.107099 9.336214 10.377070 10.913731 10.012413 11.655663 9.197286
137 138 139 140 141 142 143 144
9.895577 8.992575 11.062182 10.928292 11.173204 9.290713 9.462250 9.815623
145 146 147 148 149 150 151 152
10.567132 10.041853 12.438193 12.837043 11.155833 11.068409 11.568628 10.646408
153 154 155 156 157 158 159 160
11.120305 10.674787 11.342914 11.600863 9.872202 12.933636 12.330424 10.674265
161 162 163 164 165 166 167 168
10.692636 8.591527 8.483559 8.277465 9.219110 7.999004 7.325638 10.668789
169 170 171 172 173 174 175 176
10.442171 13.278721 12.987068 12.609307 12.139812 13.311952 9.560588 11.231509
177 178 179 180 181 182 183 184
9.614572 11.388626 11.027188 10.701644 10.408321 11.281993 11.952935 12.314095
185 186 187 188 189 190 191 192
11.343060 12.301626 11.670473 11.538465 11.450721 12.583606 9.908812 11.957886
193 194 195 196 197 198 199 200
12.476480 11.356784 11.408551 11.386678 11.371265 11.869010 11.386166 10.716040
201 202 203 204 205 206 207 208
13.547182 13.430563 14.488555 13.382721 11.721882 13.138956 11.617227 12.919960
209 210 211 212 213 214 215 216
11.610622 11.234236 12.441517 11.565354 11.775386 11.870380 11.612343 10.513345
217 218 219 220 221 222 223 224
11.332066 11.356102 8.622875 9.342198 10.532866 11.075768 10.814015 9.148910
225 226 227 228 229 230 231 232
10.259892 8.851762 10.150785 11.702025 11.247041 9.448320 8.715848 10.465157
233 234 235 236 237 238 239 240
9.063738 8.512195 9.359375 8.694810 12.250888 10.950829 11.172992 11.113227
241 242 243 244 245 246 247 248
12.539577 11.130235 11.520853 13.270299 12.445247 11.641586 11.084325 11.681937
249 250 251 252 253 254 255 256
12.903454 11.675062 11.868743 11.887980 12.142425 11.125280 10.206552 13.083514
257 258 259 260 261 262 263 264
12.553520 13.232212 11.590232 11.070216 11.072157 11.721994 10.595329 14.228343
265 266 267 268 269 270 271 272
13.651194 10.111261 12.956021 13.017707 10.712920 13.277355 11.914351 11.578296
273 274 275 276 277 278 279 280
12.601671 13.808564 13.137512 11.706520 11.860984 9.304048 10.849169 10.160520
281 282 283 284 285 286 287 288
10.957044 10.853018 11.595010 11.208375 11.222850 10.646720 10.875621 10.875865
289 290 291 292 293 294 295 296
12.139867 9.344793 7.829627 7.419011 10.276070 8.595271 11.984527 10.025066
297 298 299 300 301 302 303 304
11.658014 10.844432 13.668283 13.877468 11.842378 12.609642 12.315624 7.550419
305 306 307 308 309 310 311 312
10.543817 10.140751 10.640678 9.986984 10.672587 12.808831 8.608027 8.762374
313 314 315 316 317 318 319 320
9.800301 8.990358 10.913175 10.986842 9.848777 10.184492 10.730669 8.925857
321 322 323 324 325 326 327 328
9.810568 11.051639 12.301691 13.244583 12.143078 7.420562 7.181852 8.115063
329 330 331 332 333 334 335 336
7.557550 7.598764 7.963658 6.033631 8.174960 7.009403 6.547324 6.721532
337 338 339 340 341 342 343 344
10.495751 10.127753 8.447220 8.955561 9.111061 6.229223 7.721007 8.702168
345 346 347 348 349 350 351 352
9.796073 10.735891 10.674564 9.993831 9.387035 11.404517 12.718761 12.490109
353 354 355 356 357 358 359 360
12.490096 12.868844 14.159822 11.862943 12.490662 12.814318 13.292919 11.342429
361 362 363 364 365 366 367 368
11.790078 13.543314 12.475061 11.439849 9.501710 9.938767 8.662747 9.361561
369 370 371 372 373 374 375 376
7.333849 7.619211 8.424590 8.182639 8.244907 11.421981 12.598988 12.766756
377 378 379 380 381 382 383 384
10.004449 11.846089 11.484665 8.502844 9.985085 14.093239 11.022401 10.343070
385 386 387 388 389 390 391 392
10.870999 11.580658 8.164514 9.816118 13.810603 10.765304 10.679352 8.943409
393 394 395 396 397 398 399 400
11.394455 10.988983 11.911609 11.169336 10.926602 11.106484 10.975384 10.570735
401 402 403 404 405 406 407 408
10.800890 11.216585 11.003865 12.058352 8.979768 10.417642 10.840787 8.564483
409 410 411 412 413 414 415 416
10.468748 7.722598 9.024726 8.627277 8.712337 12.306801 11.259834 12.135047
417 418 419 420 421 422 423 424
12.909887 13.900961 14.613681 14.659878 14.516719 11.834130 12.835139 11.524950
425 426 427 428 429 430 431 432
11.205715 12.690535 12.366608 12.257143 11.554346 11.571765 10.268979 13.831592
433 434 435 436 437 438 439 440
12.488541 12.274712 11.792411 12.159000 11.286455 12.398744 12.720250 11.839790
441 442 443 444 445 446 447 448
12.042530 10.616712 11.592961 8.680015 10.002905 10.098331 9.303447 8.025186
449 450 451 452 453 454 455 456
8.160942 7.701500 7.573096 6.440509 8.413890 7.573817 8.654901 6.527707
457 458 459 460 461 462 463 464
9.316892 9.239795 7.577079 7.234717 7.744910 10.396131 11.349235 10.531142
465 466 467 468 469 470 471 472
11.286622 11.324207 11.904075 11.984744 11.254344 10.087881 12.491983 12.727448
473 474 475 476 477 478 479 480
11.023725 9.843285 12.532214 10.909423 11.556938 11.246725 13.678810 10.995575
481 482 483 484 485 486 487 488
13.406587 12.947436 11.536939 10.519024 10.614975 10.691272 12.606993 11.966835
489 490 491 492 493 494 495 496
11.220192 9.923407 11.012463 9.424555 10.077508 10.808538 10.687251 11.438914
497 498 499 500 501 502 503 504
12.408781 10.434905 8.167398 7.968639 7.492743 7.971856 7.794390 8.631370
505 506 507 508 509 510 511 512
7.279254 7.833077 10.330354 10.925965 10.909906 8.503572 12.117403 10.667929
513 514 515 516 517 518 519 520
10.129061 10.550327 9.918316 11.522068 11.296737 11.553654 10.476981 11.941762
521 522 523 524 525 526 527 528
10.578826 11.080807 9.211676 10.323909 9.621231 8.335038 8.188955 9.082492
529 530 531 532 533 534 535 536
8.075345 9.420944 8.314572 9.247623 8.538591 9.859266 7.647124 9.902155
537 538 539 540 541 542 543 544
8.546524 9.920558 11.604894 11.918312 12.416602 10.819737 11.466657 11.179962
545 546 547 548 549 550 551 552
11.665760 9.817793 14.172912 10.192052 11.355575 13.772991 8.847900 7.970775
553 554 555 556 557 558 559 560
7.460673 8.349559 8.135941 11.447727 11.618942 11.936942 10.918982 11.041702
561 562 563 564 565 566 567 568
9.949377 11.499303 10.904615 11.689807 11.747444 11.380585 11.009586 10.850464
569 570 571 572 573 574 575 576
11.602371 11.551376 12.485626 11.270907 10.170153 10.619552 9.784335 8.033726
577 578 579 580 581 582 583 584
10.810373 8.993775 5.743434 8.959191 8.089329 6.061699 8.339742 6.931294 #can also get the values using the augment function
wf_fitted_values <-augment(wf_fit[["fit"]], data = juiced_train) %>%
select(value, .fitted:.std.resid)
wf_fitted_values# A tibble: 584 x 8
value .fitted .se.fit .resid .hat .sigma .cooksd .std.resid
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 9.60 9.46 0.375 0.136 0.0324 2.09 0.00000433 0.0663
2 10.8 10.4 0.383 0.371 0.0338 2.09 0.0000338 0.181
3 11.2 11.8 0.404 -0.583 0.0376 2.09 0.0000936 -0.285
4 12.4 11.1 0.388 1.24 0.0346 2.08 0.000384 0.604
5 10.5 10.9 0.426 -0.355 0.0418 2.09 0.0000388 -0.174
6 15.6 11.1 0.379 4.50 0.0332 2.08 0.00486 2.20
7 12.4 10.1 0.459 2.33 0.0485 2.08 0.00196 1.14
8 11.1 8.19 0.777 2.91 0.139 2.08 0.0108 1.51
9 14.6 11.5 0.378 3.03 0.0329 2.08 0.00219 1.48
10 12.0 10.6 0.452 1.33 0.0470 2.08 0.000623 0.656
# … with 574 more rows[1] TRUE## Let's make a plot of fitted and real values
ggplot(wf_fitted_values, aes(x = .fitted, y = value)) + geom_point()
Ok, so our fitted range appears to be smaller than the real values. We could probably do a bit better.
At this point we could take a look at the accuracy of our model performance, but we will only have one reference point: our testing dataset. And we haven’t done any tuning of our model or cross validation… so generally speaking you should not do this.
However if you were short on time you could continue like this.
Using the workflows method, you would need functions like this: tune::tune_*(), tune::fit_resamples() or tune::last_fit() from the tune package to get an assessment of fit.
We could stop here and use the yardstick package to evaluate performance. First we would want to use the model to predict values for the monitors in the testing data.
Using parsnip we need to use the baked data testing data.
baked_test_pm_ready <-baked_test_pm %>%select( -"id", -"fips")
values_pred_parsnip <-predict(PM_fit, baked_test_pm_ready)
values_pred_parsnip# A tibble: 292 x 1
.pred
<dbl>
1 10.4
2 10.5
3 10.3
4 10.4
5 10.6
6 12.9
7 9.53
8 9.47
9 8.82
10 7.67
# … with 282 more rows# using the workflows version
values_pred_wfs <-
predict(PM_wflow_fit, test_pm) %>%
bind_cols(test_pm %>% select(value, fips))
values_pred_wfs# A tibble: 292 x 3
.pred value fips
<dbl> <dbl> <fct>
1 10.4 11.7 1049
2 10.5 13.1 1073
3 10.3 12.2 1073
4 10.4 12.2 1089
5 10.6 11.4 1103
6 12.9 12.2 1121
7 9.53 10.9 4013
8 9.47 10.6 4021
9 8.82 14.1 4023
10 7.67 5.83 4025
# … with 282 more rowsLet’s take a look at how well it did:
Say we were done optimizing our parameters we could then use the last_fit() function of the workflows package.
overallfit <-tune::last_fit(PM_wflow, pm_split)
# or
overallfit <-PM_wflow %>%
tune::last_fit(pm_split)
##overallfitWe could check out test performance using the collect_metrics() function of the tune package.
model performance :https://medium.com/@limavallantin/metrics-to-measure-machine-learning-model-performance-e8c963665476
Here you can see the predictions for the test set (the 292 rows with predicitions out of the 876 original monitor values) also using the tune package with the collect_predictions() function.
However we would really want to tune parameters and use cross validation for this.
yardstick can’t talk directly to workflows… need tune for that…
We will use the rsample package again in order to further implement what are called cross validation techniques. This is also called resampling or repartioning. Note: we are not actually getting new samples from the underlying distribution so the term resampling is a bit of a misnomer.
Cross validation splits our training data into multiple training data sets to allow for an assessment of the accuracy of the model.
Here is a visualization of the concept for cross validation/resampling/repartitioning from Max Kuhn:
Technically creating our testing and training set out of our original training data is sometimes considered a form of cross validation called the holdout method. As we just learned this can give us a better sense of the accuracy of our data in a more generalizable way.
However, we can do a better job of optimizing our model for accuracy if we also perform another type of cross validation on the newly defined training set that we just created. There are many cross validation methods and most can be easily implemented using rsamples package. We will use a very popular method called either k-fold or v-fold cross validation.
This method involves essentially preforming the hold out method iteratively with the training data.
First the training set is divided into k or v equally sized smaller pieces.
Then the model is trained on the model on k-1 or v-1 subsets of the data iteratively (removing a different v or k untill all possible k-1 or v-1 sets have been evaluated) to get a sense of the performance of the model. This is really useful for fine tuning specific aspects of the model in a process called model tuning.
Here is a visualization of how the folds are created:
Note: People typically ignore spatial dependence with cross validation of air pollution monitoring data in the air pollution field, so we will do the same. However, it might make sense to leave out blocks of monitors rather than random individual monitors to help account for some spatial dependence.
The vfold_cv() function of the rsample package can be used to parse the training data into folds for k-fold/v-fold cross validation.
The v argument specifies the number of folds to create. The repeats argument specifies if any samples should be repeated across folds - defualt is FALSE The strata argument specifies a variable to stratify samples across folds (just like in initial_split()).
Again because these are created at random, we need to use the base set.seed() function in order to obtain the same results each time we knit this document. Generally speaking using 10 folds is good practice, but this depends on the variablity within your data. We are going to use 4 for the sake of expediency.
# 4-fold cross-validation
# A tibble: 4 x 2
splits id
<list> <chr>
1 <split [438/146]> Fold1
2 <split [438/146]> Fold2
3 <split [438/146]> Fold3
4 <split [438/146]> Fold4NULLNULLOnce the folds are created they can be used to evaluate peformance by fitting the model to each of the resamples that we created:
We can fit the model to our cross validation folds using the fit_resamples() function of the tune package, by specifying our workflow object and the cross validation fold object we just created. See here for more information.
control <- control_resamples(save_pred = TRUE)
resample_fit <-tune::fit_resamples(PM_wflow, vfold_pm)We can now take a look at various metrics of performance based on the fit of our 10 cross validation “resamples”. To do this we will use the show_best() function of the tune package.
# A tibble: 1 x 5
.metric .estimator mean n std_err
<chr> <chr> <dbl> <int> <dbl>
1 rmse standard 2.18 4 0.0763Now let’s try some tuning.
Let’s take a closer look at how the monitor values vary with latitude and longitude.
train_pm %>%
dplyr::select(value, lon, lat) %>%
tidyr::pivot_longer(cols = c(lon, lat),
names_to = "predictor", values_to = "loc_value") %>%
ggplot(aes(x = loc_value, value)) +
geom_point(alpha = .2) +
geom_smooth(se = FALSE) +
#scale_y_log10() +
facet_wrap(~ predictor, scales = "free_x")
We can see that there does not appear to be a single linear relationship for either of these predictors. Thus we might want to think about using splines or this(https://towardsdatascience.com/numerical-interpolation-natural-cubic-spline-52c1157b98ac) or just this(https://tidymodels.github.io/tune/articles/getting_started.html) or this(https://www.psych.mcgill.ca/misc/fda/ex-basis-b1.html) to model the relationship in our training data more closely. For example for the latitude plot (left) if we had 2 lines and one breakpoint called a knot around 40, with the first line having a positive slope and the second with a negative slope this would fit the data more similarly to the blue line shown in the figure.
We can tune for the number of knots by using a step function in the recipes package called step_ns() where ns stands for natural splines. In order to tune for the number of knots or degrees of freedom, we can set the deg_free argument to tune(). This is helpful, becuase we aren’t exactly sure how closely we should be following the relationship with the value and our longitude and latitude data in our training data to achieve good accuracy yet keep our model generalizable for other data.
This is when our cross validation methods become really handy. We can test out different values for the deg_free argument and see how our model performance varies across our training folds to try to find the optimal value.
We will update our recipe to add these steps. It is a good idea to do this for individual predictors because you can name each with the tune argument so that you can keep track of it later. We can see what we intend to tune with the parameters() function of the dials package.
See here for more information about implementing this in tidymodels.
novel_rec %<>%
step_ns(lon, deg_free = tune("lon df")) %>%
step_ns(lat, deg_free = tune("lat df"))
# novel_rec %<>%
# step_ns(lat, deg_free = tune())
# novel_rec
pm_param <-dials::parameters(novel_rec)
pm_paramCollection of 2 parameters for tuning
id parameter type object class
lon df deg_free nparam[+]
lat df deg_free nparam[+]Genearlly you could use the grid_*() functions of the dials package to create the different combinations of degrees of freedom to test for both variables to optimize the model. In our case we can visably see that if we add more than say 4 or 5 degrees of freedom we will likely overfit the data. So instead of using these functions we will create our own grid using the base seq() and expand.grid() functions.
#an example of what you could do:
#spline_grid <-dials::grid_regular(pm_param, levels = 3)
df_vals <- seq(1, 5, by = 2)
spline_grid <- expand.grid(`lon df` = df_vals, `lat df` = df_vals)
spline_grid lon df lat df
1 1 1
2 3 1
3 5 1
4 1 3
5 3 3
6 5 3
7 1 5
8 3 5
9 5 5Now we will tune this hyper-parameter (degrees of freedom) for both the lat and lon variables using our cross validation folds. To do this we will use the tune_grid() function of the tune package.
df_tuning <-lm_PM_model %>%
tune::tune_grid(novel_rec, resamples =vfold_pm,
grid = spline_grid)
#df_tuning <-PM_wflow %>% tune::tune_grid(resamples =vfold_pm,
# grid = spline_grid,
# param_set =pm_param)
df_tuning# 4-fold cross-validation
# A tibble: 4 x 4
splits id .metrics .notes
<list> <chr> <list> <list>
1 <split [438/146]> Fold1 <tibble [18 × 5]> <tibble [18 × 1]>
2 <split [438/146]> Fold2 <tibble [18 × 5]> <tibble [18 × 1]>
3 <split [438/146]> Fold3 <tibble [18 × 5]> <tibble [18 × 1]>
4 <split [438/146]> Fold4 <tibble [18 × 5]> <tibble [18 × 1]># A tibble: 18 x 7
`lon df` `lat df` .metric .estimator mean n std_err
<dbl> <dbl> <chr> <chr> <dbl> <int> <dbl>
1 1 1 rmse standard 2.18 4 0.0763
2 1 1 rsq standard 0.361 4 0.0486
3 1 3 rmse standard 2.13 4 0.0807
4 1 3 rsq standard 0.383 4 0.0388
5 1 5 rmse standard 2.13 4 0.0812
6 1 5 rsq standard 0.386 4 0.0403
7 3 1 rmse standard 2.10 4 0.0613
8 3 1 rsq standard 0.402 4 0.0296
9 3 3 rmse standard 2.05 4 0.0709
10 3 3 rsq standard 0.428 4 0.0191
11 3 5 rmse standard 2.03 4 0.0656
12 3 5 rsq standard 0.439 4 0.0197
13 5 1 rmse standard 2.11 4 0.0616
14 5 1 rsq standard 0.397 4 0.0258
15 5 3 rmse standard 2.05 4 0.0739
16 5 3 rsq standard 0.427 4 0.0164
17 5 5 rmse standard 2.02 4 0.0717
18 5 5 rsq standard 0.442 4 0.0153# A tibble: 18 x 7
`lon df` `lat df` .metric .estimator mean n std_err
<dbl> <dbl> <chr> <chr> <dbl> <int> <dbl>
1 1 1 rmse standard 2.18 4 0.0763
2 1 1 rsq standard 0.361 4 0.0486
3 1 3 rmse standard 2.13 4 0.0807
4 1 3 rsq standard 0.383 4 0.0388
5 1 5 rmse standard 2.13 4 0.0812
6 1 5 rsq standard 0.386 4 0.0403
7 3 1 rmse standard 2.10 4 0.0613
8 3 1 rsq standard 0.402 4 0.0296
9 3 3 rmse standard 2.05 4 0.0709
10 3 3 rsq standard 0.428 4 0.0191
11 3 5 rmse standard 2.03 4 0.0656
12 3 5 rsq standard 0.439 4 0.0197
13 5 1 rmse standard 2.11 4 0.0616
14 5 1 rsq standard 0.397 4 0.0258
15 5 3 rmse standard 2.05 4 0.0739
16 5 3 rsq standard 0.427 4 0.0164
17 5 5 rmse standard 2.02 4 0.0717
18 5 5 rsq standard 0.442 4 0.0153# A tibble: 1 x 7
`lon df` `lat df` .metric .estimator mean n std_err
<dbl> <dbl> <chr> <chr> <dbl> <int> <dbl>
1 5 5 rmse standard 2.02 4 0.0717We can create another workflow to see how model pefromance compares using a different model. In this case we are going to peform something called Principal Component Analysis or PCA.
So what is PCA?
lm_PCA_rec <-recipe(train_pm) %>%
update_role(everything(), new_role = "predictor")%>%
update_role(value, new_role = "outcome")%>%
update_role(id, new_role = "id variable") %>%
update_role("fips", new_role = "county id") %>%
step_dummy(state, county, city, zcta) %>%
step_pca(all_predictors()) Let’s take a look to see what the step_pca function does to our predictors. To do so recall that we need to use the prep and juice functions of the recipes package on our recipe.
oper 1 step dummy [training]
oper 2 step pca [training]
The retained training set is ~ 0.13 Mb in memory.Rows: 584
Columns: 8
$ id <fct> 1003.001, 1027.0001, 1033.1002, 1055.001, 1069.0003, 1073.0023,…
$ value <dbl> 9.597647, 10.800000, 11.212174, 12.375394, 10.508850, 15.591017…
$ fips <fct> 1003, 1027, 1033, 1055, 1069, 1073, 1073, 1073, 1073, 1073, 107…
$ PC1 <dbl> -4120232815, -1570558844, -1534934869, -1388102571, -1504354268…
$ PC2 <dbl> -118909004, -346706197, 10140574, -129802253, -136385028, 23433…
$ PC3 <dbl> -72827.994, 7132.812, -56957.316, 45519.861, 36487.258, 448189.…
$ PC4 <dbl> -20385.63273, 1615.38773, -7187.37037, -15876.58640, -25852.952…
$ PC5 <dbl> -846.027447, 90.287809, 171.426032, -576.131718, -926.823714, -…We still want to use the lm package for our regression so we can use the same model object:
Linear Regression Model Specification (regression)
Computational engine: lm pca_wflow <-workflows::workflow() %>%
workflows::add_recipe(lm_PCA_rec) %>%
workflows::add_model(lm_PM_model)
pca_wflow══ Workflow ═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: linear_reg()
── Preprocessor ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2 Recipe Steps
● step_dummy()
● step_pca()
── Model ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Linear Regression Model Specification (regression)
Computational engine: lm Remember that using workflows we dont actually need to prep our recipe, we can just fit our model directly. So now we will use tune to fit our resamples… WAIT DOES THIS WORK?? or do you need to use fit…
Fit the cross validation samples:
Look at the performance:
# A tibble: 2 x 5
.metric .estimator mean n std_err
<chr> <chr> <dbl> <int> <dbl>
1 rmse standard 2.76 4 0.271
2 rsq standard 0.0527 4 0.0184And we can compare this with our previous performance:
# A tibble: 2 x 5
.metric .estimator mean n std_err
<chr> <chr> <dbl> <int> <dbl>
1 rmse standard 2.18 4 0.0763
2 rsq standard 0.361 4 0.0486So we can see that our performance isn’t quite as good - especially if we look at the rmse value.
Let’s review everything:
check_new_values: This check will break the bake function if any of the checked columns does contain values it did not contain when prep was called on the recipe. If the check passes, nothing is changed to the data
check_range creates a specification of a recipe check that will check if the range of a numeric variable changed in the new data.
prepper for cross validation?
great blog about cross validation etc https://towardsdatascience.com/train-test-split-and-cross-validation-in-python-80b61beca4b6
We have evaluated average consumption estimates of 15 dietary factors with probably non-communicable disease (NCD) risk from 195 different countries around the world. To do so we imported data from a PDF using the pdftools package, as well as data from two CSV files using readr. We used tidyverse packages such as dplyr, stringr, and tidy to clean and join the data from the PDF with the CSV files.
We learned that Regression is a powerful and flexible statistical tool that simplifies or estimates the relationships between variables using a mathematical model. We learned about the utility of the regression to compare groups, look for associations between variables, and to predict outcomes based on multiple predictor or explanatory variables. We then compared this to other popular tests like the \(t\)-test and the ANOVA. We learned that these tests are actually equivalent to specialized types of regressions.
Our statistical analysis focused on evaluating differences in the consumption of red meat around the world between females and males and across different age groups. First we looked at the assumptions of \(t\)-tests and regressions, and determined that the relative percentage data of red meat consumption to the optimal guideline suggested amount was right skewed. We learned that we could transform the data by taking the log of these values to achieve more normally distributed data. To compare males and females we used a \(t\)-test and learned that a \(t\)-test is a specialized form of a linear regression. To compare the 15 different age groups we used an ANOVA and learned that the ANOVA is also a specialized form of linear regression. We examined how we obtained the same results using either statistical test. This was also the case if we looked at the effect of gender and controlled for the paired country structure in the data by either including location_name in the model as another term or by using a mixed effects model to control for this structure as a random effect but not specifically test for the influence of location_name on red meat consumption estimates. We learned that fixed effects are those that we wish to evaluate, while random effects are those that may influence the relationships of our variables of interest but that we do not wish to actively evaluate. Using these tests and models, we determined that males consume more red meat than women on average around the world.
Our ANOVA analysis of age determined that indeed there at least one age group consumed a significantly different amount of red meat compared to the other age groups, and this was still the case when we controlled location_name. However, we learned that we could that the ANOVA does not provide information about which age groups are different. We learned how the regression however could provide some comparisons of different age groups relative to the reference age group. Furthermore, our data visualizations allowed us to determine that in general red met consumption appears to be higher in the younger age groups relative to the older age groups.
Finally, we also looked at differences in red meat consumption between the different countries and saw in our ANOVA analysis and our regression analysis that there were significant differences. We were able to use a regression that included sex, age_group_name, and location_name to evaluate the influence of each of the three demographic factors on consumption while controlling or accounting for the other two. Our results demonstrated that all three influenced or were associated with red meat consumption.
In preforming our statistical analyses we learned about the assumptions of the \(t\)-test, the regression, and the ANOVA. We also learned about important methods to tests these assumptions.
We can evaluate if our data is normally distributed by plotting the distribution and by creating [Q-Q plots](Q-Q Plots to compare the distribution of our data to the theoretical normal distribution.
If our data is not normally distributed, we can consider these options:
See this case study for more information on \(t\)-test assumptions.
We learned that we can test if 2 groups have equal variance using:
1) the F test with var.test()
2) Mood’s test using mood.test() (use if the data is not normally distributed)
L (linear) - There is a linear relationship between the variables.
I (independent) - The samples are independent from one another.
N (normal) - The residuals are normally distributed.
E (equal variances) - The variance of the residuals of the groups is similar.
It is also important that predictor variables are not correlated with one another.
We learned about three tests for examining the equality of variance of 3 or more groups: 1) Bartlett’s test (works well if the data appears to be normally distributed) 2) Fligner-Killeen test is nonparametric and does not assume normality 3) Levene’s test, is more robust to violations of normality than the Bartlett’s test, but not as robust as the Fligner- Killeen test
Using the ggplot2 package we were able to visualize trends in the data and to compare consumption of these dietary factors in the US with that of the other countries. We see that the populations in many countries are over-consuming foods that are associated with health risk when over-consumed. In particular processed meat and sugar-sweetened beverages appear to be the most over consumed. Importantly both of these appear to be consumed at higher quantities by males and younger adults. People in the US appear to consume less sugar-sweetened beverages than other countries, however, people are still over-consuming. Processed meat however appears to be especially bad in the US. In terms of food that need to be consumed in adequate amounts to overcome health risk, nearly all countries for all factors are not reaching guideline levels. However, there are some countries consuming more than adequate amounts of legumes, vegetables, fruits and fiber. People in the US appear to eat more milk products and consume more omega-3 fatty acid and calcium rich foods than other countries. All countries including the US consume very low levels of polyunsaturated fatty acids. These polyunsaturated fatty acids are abundant in seeds, nuts, avocados, as well as fish. Likely the low level of consumption of nuts and seeds contributes to these low polyunsaturated fatty acid estimates. The supplementary table included in the article suggests that poor consumption of polyunsaturated fatty acids is associated with ischemic heart disease. The article takes this data further to evaluate the association of consumption levels of these foods with mortality.
Analyses like the one in our case study are important for defining which groups could benefit the most from interventions, education, and policy changes when attempting to mitigate public health challenges. You can see in the article however that many additional considerations would be involved to perform a more thorough analysis to adequately understand the data enough to recommend policy changes.
Students can evaluate consumption estimates of another dietary factor besides red meat.
review of tidymodels
guide for preprocessing with recipes
guide for using GGally to create correlation plots guide for using parsnip to try different algorithms or engines recipe functions
Terms and concepts covered:
Tidyverse
RStudio cheatsheets
Inference
Regression
Different types of regression
Ordinary least squares method
Residual
Packages used in this case study:
| Package | Use |
|---|---|
| here | to easily load and save data |
| readr | to import the CSV file data |
| dplyr | to arrange/filter/select/compare specific subsets of the data |
| skimr | to get an overview of data |
| summarytools | to get an overview of data in a different style |
| pdftools | to read a PDF into R |
| magrittr | to use the %<>% pipping operator |
| purrr | to perform functions on all columns of a tibble |
| tibble | to create data objects that we can manipulate with dplyr/stringr/tidyr/purrr |
| tidyr | to separate data within a column into multiple columns |
| ggplot2 | to make visualizations with multiple layers |
Do I need to talk about machine learning in general more… classification vs prediction?